1. Bargaining Behaviour at the Grand
Bazaar of Istanbul
Bachelor’s Thesis
supervised by the
Department of Economics at the University of Zurich
Prof. Dr. María Sáez Martí
to obtain the degree of
Bachelor of Arts UZH (in Economics)
Author: Batuhan Kalyoncu
Course of Studies: Economics
Student ID: 10-918-936
Address: Gubelstrasse 44
8050 Zurich
E-Mail: batuhan.kalyoncu@uzh.ch
Closing date: May 19, 2016
3. Abstract
T
his thesis analyses the bargaining behaviour at the Grand Bazaar
of Istanbul. This study examines how real-life bargaining processes
can be modelled using game theoretic approaches with focus on
bargaining powers and reservation values. First, basic concepts of game
theory are introduced and negotiation processes are described, followed by
multiple possible modifications of bargaining games. Finally results of an
on site field research are presented and their meaning for the bargaining
models are explained. These results give insights into how some buyers’
characteristics affect sellers’ price settings and how potential customers
can avoid inflated prices.
iii
5. Acknowledgments
F
irst and foremost, I want to thank my supervisor Prof. Dr. María
Sáez Martí for introducing me to the fascinating world of game
theory and for her continuous feedback and support. Additionally,
I want to thank Numan Hocao˘glu, member of the Istanbul chamber of
commerce, and his son Selman, for introducing me to the right people
at the Grand Bazaar. It would have been impossible to conduct my
survey without them. Specially I want to mention the ongoing support
of my parents, Leyla Görpe and Ibrahim Kalyoncu, and my manager at
work Laura Ameti, without whom my studies at the University of Zurich
would not have been possible. I am especially grateful for my girlfriend
Seher Ilciktay’s and Daniel Dürr’s support and motivation in times of
doubt. Additionally, I want to thank Christian Rösch and Tim Naef for
proofreading and giving my thesis the final touch. Last but not least, I
want to thank Sebastian Pinegger and Janosh Köfferli for their support
and feedback during the evaluation and implication of the collected data.
v
15. Chapter 1
Introduction
M
ost of the tourists in Turkey probably know that negotiation
at a bazaar is totally normal. It is one of the biggest and most
important parts of a merchant’s job and his ability of negotiation
can determine how big his revenue will be at the end of the day. Therefore,
how should a tourist who is visiting the Grand Bazaar of Istanbul prepare
for shopping? He1 could simply go to a store in the Bazaar and ask for a
price, then negotiate until a price is reached which he thinks is fair based
on some exogenous beliefs about the product’s value. The tourist would
probably be better off trying to predict the prices from some knowledge
about the industry. In particular, a tourist could do some research and
find out how much it costs to produce a product. He could invest some
time in bargaining with different vendors for similar products to gain
more information. He could also try to hide some of his characteristics.
For instance, a very wealthy tourist would be advised to leave his Rolex
in the hotel safe to achieve a better bargaining outcome. This thesis has
two goals, one is to find out whether or not a real-life bargaining situation
at the Grand Bazaar can be modelled with a game theoretic approach
and the other is how certain buyers’ characteristics might influence sellers’
price settings and therefore the bargaining outcome.
Firstly, chapter 2 will introduce the concept of game trees. They are a
1For simplicity and in order to avoid gender discrimination, the players in the games
will be masculine throughout the thesis.
1
16. 2 CHAPTER 1. INTRODUCTION
common way to describe a game with multiple rounds and two players.
A game displayed with a game tree is called an extensive-form game. In
chapter 3, the focus will lie on the negotiators’ strategies and how some
may outperform the others, followed by an introduction to the concept of
the Nash equilibrium. Chapter 4 will illustrate how a Nash equilibrium
can be found using backward induction. This concept is commonly used
to analyse extensive-form games in detail. It should be noted that not all
the Nash equilibria are reasonable in continuous games. For instance, if a
tourist threatens a seller that he will buy the same good at his competitor
(who happens to be more expensive) unless he gives him a discount of
20%, this would be an "empty threat". Strategies like that would not be
optimal to carry out. To rule out such strategies, Selten (1965) introduced
his concept of subgame perfection. In chapter 5, the attention will be
focussed to games with imperfect information, where players are unsure
about their opponents’ payoffs. Regarding the initial situation at a bazaar,
this will be more realistic.
In chapter 6, the model of cooperative bargaining games will be dis-
cussed, introducing the Nash bargaining model and its axioms to build
the foundation for the non-cooperative bargaining games. In chapter 7
an ultimatum game will be analysed followed by a closer look at the
Rubinstein’s alternating-offers model. It will be showed how equilibria
in a model with asymmetric information depend on bargaining power
and how this power is affected by reputation effects. After learning more
about some basic bargaining models, it will be interesting to observe how
these models work in a real-life situation. There are just a few places
on earth like the Grand Bazaar of Istanbul where bargaining has such a
long-standing tradition. Chapter 8 will contain some background infor-
mation about the Grand Bazaar’s history and provide some insights on
the sellers’ mentality and the Turkish culture. In Chapter 9, the conducted
field research at the Grand Bazaar will be explained and presented. This
thesis will be concluded by the discussion of how buyers’ attributes affect
the price settings of sellers and what a tourist should pay attention to
before shopping at the Grand Bazaar.
17. Chapter 2
Extensive-Form Games
I
n this chapter, a graphical way of describing games will be introduced.
Games in this form are called extensive-form games. A game in extensive
form depicts the rules of the game, the order in which the players
take action, all the information available when it is their move and the
payoffs at any terminal point. An extensive-form game is portrayed by a
game tree and its starting point is called the root. All the outgoing edges
from the root end in vertices which represent different positions in the
game. Vertices without outgoing edges are terminal positions where the
game ends, also called the leaves. Every terminal vertex has a payoff for
each player defining their outcomes if the game ends at this position.
Non-terminal vertices represent either a move by "Nature"1 or a position
in the game where one of the players needs to move. There are always
probability distributions at every Nature-move vertex for every possible
track emerging from it.
In a game with imperfect information, players do not necessarily know
their position. If a player could be at more than one vertex, given the
information he has at this stage of the game, the combination of all vertices
he could be positioned at is called an information set.2 On the contrary, in a
game with perfect information, every player always knows his position and
1e.g. a toss of a coin or a die
2e.g. blackjack; one card is always hidden from the players, therefore it is impossible
for them to know at which point in a game they are located at.
3
18. 4 CHAPTER 2. EXTENSIVE-FORM GAMES
every move which had led to it when he is called to take action.
A player’s strategy is any action he could choose at any information
set and it will determine his action at any stage of the game. In a game
with no moves by Nature, the strategies of the players determine a path
from the root to a leaf which is called the play of a game. If there are
moves by Nature there will be several plays with corresponding probability
distributions over the possible outcomes of the game. (Maschler, Solan, &
Zamir, 2013, p. 39-42)
Even if the players have different information at various locations at
the game, it is crucial that they have a shared understanding of the game
as a whole. They need to know how the game looks and that at some
point in the game some players may not be able to distinguish between
nodes in the same information set. This shared understanding of the game
is called common knowledge and is defined as follows:
Definition 1 [COMMON KNOWLEDGE]: A particular fact F is said to be
common knowledge between the players if each player knows F, each player
knows that the others know F, each player knows that every other player knows
that each player knows F, and so on. (Watson, 2013, p. 44)
2.1 Game Trees
Imagine a tourist must decide between going to the Grand Bazaar and
staying at his hotel room. This decision tree would look like the one in
Figure 1. The upper node is the start of the game and is thereby the initial
node where the tourist needs to decide whether to stay or leave. Every
extensive-form game always has only one initial node. The tourist has
only two possible strategies: STourist = {Stay, Leave}. This is a convention
where all possible strategies are written as a vector.
If the tourist decides to go to the Grand Bazaar, he will walk past a
lot of shops where sellers need to decide between waiting for the tourist
to enter and trying to lure him in. The tourist then can decide whether
to go in or not. Figure 2 shows how the decision tree expands with the
19. 2.1. GAME TREES 5
Tourist
Stay Leave
Figure 1: First decision
added possibilities of choices. Additionally, there are now payoffs under
every node without outgoing branches. Those are terminal nodes and
their payoffs determine the order of preference for each player. The payoffs
or utilities in economic games are often about monetary rewards. In this
example, the utilities are simply transformed into made up numbers. It
will be pretended that every store in the Grand Bazaar has something
interesting in it and finding it brings a payoff of 10 to a tourist. On the
contrary, leaving his hotel room costs him 5, because it is an effort to get
out of a comfortable hotel bed. Additionally, the tourist in this example
loves attention and therefore likes it when sellers approach him. This
increases his output by 5. However, to lure a tourist in is hard work for a
seller and costs him 5, whereas a tourist coming into his store gives him a
payoff of 10.
In the example of Figure 2, it can be stated that if the tourist leaves his
hotel room and the seller waits for the tourist to come in, who actually
then enters the shop, by following the branches it can be observed that
the tourist will get a payoff of 5 and the seller a payoff of 10. It is a
common convention that the first number is the first player’s payoff, in
this example the tourist. Note that a differentiation is needed between the
two Go in’s and the two Stay out’s. An apostrophe has been introduced to
do so. This way it is possible to just name a player and an action to define
where exactly in the tree it is referred to. The tourist now has 8 different
strategies: STourist ={(Stay, Go in, Go in’), (Stay, Go in, Stay out’), , (Stay,
Stay Out, Go in’), (Stay, Stay out, Stay out’), (Leave, Go in, Go in’), (Leave,
Go in, Stay out’), (Leave, Stay out, Go in’), (Leave, Stay out, Stay out’)},
while the seller has two: SSeller ={Wait, Lure}. (Watson, 2013, p. 10-13)
20. 6 CHAPTER 2. EXTENSIVE-FORM GAMES
Tourist
(0, 0)
Stay
Seller
Tourist
(5, 10)
Go in
(−5, 0)
Stay out
Wait
Tourist
(10, 5)
Go in’
(0, −5)
Stay out’
Lure
Leave
Figure 2: Adding the seller
2.2 Games with Imperfect Information
Whereas in games similiar to the one in Figure 2, where every player
exactly knows at which vertex in the game tree the game is currently at,
in most games this is not the case. Games in which a player does not have
perfect knowledge of actions prior to that stage of the game are called
games with imperfect information. In Figure 3, the seller does not know if
the tourist is eager to buy or not. He needs to decide whether he offers
the tourist a high or low price for certain goods. The ellipse surrounding
the seller’s two vertices represents the fact that when it is his turn to
take action, he does not know on which vertex he currently is. In this
game both players only have two strategies: STourist ={Eager to buy, Not},
SSeller ={High, Low} (Maschler et al., 2013, p. 52)
21. 2.3. EXTENSIVE-FORM GAMES IN STRATEGIC-FORM 7
Tourist
(0, 10)
High
(5, 5)
Low
Eager to buy
(0, 0)
High
(5, 5)
Low
Not
Seller
Figure 3: Imperfect information
Seller
Tourist
Eager to buy Not
High (0,10) (0,0)
Low (5,5) (5,5)
Figure 4: The strategic-form of Figure 3
2.3 Extensive-Form Games in Strategic-Form
It is possible to draw all extensive-form games in strategic-form. The
strategic-form is described by matrices and looks like Figure 4. The
different players and their strategies are outside of the matrix and the
different payoffs are inside. If a path to a terminal point is followed, for
instance, the path on the left hand side (Eager to buy & High), the payoff
at that leaf can be compared to the one in the matrix where row "High"
intercepts with column "Eager to buy".
It is very important to depict every single strategy of all the players
when drawing a game tree to its strategic-form. For example, transforming
Figure 2 in its strategic-form would look like Figure 5, where S stands
for "Stay", G for "Go in", L for "Leave" and SO for "Stay out". It is easier
to find some properties like dominance and Nash equilibria by using the
strategic-form. Those properties will be elaborated in the next chapter.
23. Chapter 3
Dominance, Best Response and
Nash Equilibrium
T
his chapter introduces three of the most important concepts of
game theory. They are the foundation of most theories of rational
behaviour1 and crucial for finding ideal strategies. A game has
always three elements: the set of players i ∈ I, which will always be
a finite set {1, 2, ...I} regarding a situation at a bazaar, the pure-strategy
space Si for each player i, and the payoff functions ui(s) for each profile
s = (s1, ..., sI) of strategies. Pure strategy means that a player will choose
one strategy certainly or with p = 1. Any time p = {0, 1} it is referred
to a mixed strategy σ. If a player chooses action A and B randomly with
p between 0 and 1, the numbers p and 1 − p constitute a probability
distribution over the set {A, B}. Whenever it is referred to all players
except player i, they will be denoted by "−i". (Fudenberg and Tirole,
(1991), p. 4; Watson, (2013), p. 37)
1Each player chooses the strategy which leads to the outcome he prefers the most.
Classic game theory assumes that players are perfect calculators and make no mistakes
following their best strategy.
9
24. 10 CHAPTER 3. DOMINANCE, BEST RESPONSE & NE
Tourist
(5, 10)
Go in
(−5, 0)
Stay out
Figure 6: Go in dominates Stay out
3.1 Dominance
The bottom part of the left hand side of Figure 2 will be used to explain
dominance. It is perfectly clear that, when it is the tourist’s turn to take
action at the root shown in Figure 6, he will always decide to go in. The
same applies to the decision node at the same level on the right hand side
of Figure 2.
In a game like shown in Figure 7, where seller and tourist basically
choose their strategies at the same time, strategy "Go in" has an interesting
property. Regardless of the seller’s strategy, "Go in" always results in a
higher payoff than "Stay out". In cases like these, where one strategy is
always better independent of other players’ strategies, technically it is
stated that "Stay out" is strictly dominated by "Go in", and thus "Stay out"
should never be played by a rational player. Note that the seller also has
a dominated strategy. If the tourist decides to go in, he should wait and
if the tourist decides to stay out, he should wait again. This means that
strategy "Lure" is strictly dominated by "Wait".
Definition 2 [DOMINANCE]: A pure strategy si of player i is dominated if
there is a strategy (pure or mixed) σ ∈ ∆Si such that ui(σi, s−i) > ui(si, s−i),
for all strategy profiles s−i ∈ S−i of the other players. (Watson, 2013, p. 49-50)
For Dominance there must be a strict inequality in the equation, but there
is a version which needs to be considered based on a weaker condition.
25. 3.1. DOMINANCE 11
Seller
(10, 5)
Go in
(0, −5)
Stay out
Wait
(5, 10)
Go in
(−5, 0)
Stay out
Lure
Tourist
Figure 7: Go in dominates Stay out again
Definition 3 [WEAKLY DOMINATED]: The strategy si is weakly domi-
nated if there exists a σi such that the inequality in Definition 1 holds with weak
inequality, and the inequality is strict for at least one s−i. (Maschler et al., 2013,
p. 90)
It gets even clearer by using the strategic-form of Figure 7. You can
compare the seller’s payoffs in the top row with the corresponding payoffs
in the bottom row. The same is possible with the tourist’s columns. Usually
dominated rows and columns are crossed out, since they do not have to
be considered any longer for the rest of the game. Eliminating them may
reveal new dominated strategies.
Seller
Tourist
Go in Stay out
Wait (10,5) (0,-5)
Lure (5,10) (-5,0)
Figure 8: The strategic-form of Figure 7
26. 12 CHAPTER 3. DOMINANCE, BEST RESPONSE & NE
3.2 Best Response
Many games do not have any dominated strategies or an elimination of
dominated strategies does not yield a unique outcome. In such cases, a
different way to find a solution to the game is to be used. For each strategy
of one player, the best response of the other has to be considered. Each
and every move of one player has to be evaluated to find the best possible
choice. Using this method, called the best-response analysis for every player,
all possible Nash equilibria of a game can be located. (Dixit, Skeath, &
Reiley, 2015, p. 106)
Definition 4 [BEST RESPONSE]: Let s−i be a strategy vector of all the players
not including player i. Player i’s strategy si is termed a best reply to s−i if
ui(si, s−i) = max
ti∈Si
ui(ti, s−i). (Maschler et al., 2013, p. 97)
3.3 Nash Equilibrium
In cases where players’ strategies are best responses to each other, in other
words, if the players have "mutual best responses", where no one has an
incentive to deviate from his strategy, the term Nash equilibrium2is used in
this terminal point of the game. (Watson, 2013, p. 97)
Figure 9 shows a game in strategic-form without any dominated strate-
gies. The seller prefers coffee while the tourist prefers tea, but for both
of them it is important that they drink the same beverage. If the tourist
chooses "Coffee", the seller’s best response is "Coffee", but if he chooses
"Tea", the best response will be "Tea" and vice versa. The two pairs of
strategy (Coffee, Coffee) and (Tea, Tea) both satisfy a stability property.
Neither player has a reason to deviate, because given the other player’s
strategy, no deviation will grant a higher payoff.
2Nobel laureate John Nash is the "father" of the equilibrium concept which he reported
in Non-Cooperative Games, Annals of Mathematics, 1951.
27. 3.3. NASH EQUILIBRIUM 13
Seller
Tourist
Coffee Tea
Coffee (10,5) (2,2)
Tea (0,0) (5,10)
Figure 9: Tea or Coffee
Definition 5 [NASH EQUILIBRIUM]: The strategy vector s∗ = (s∗
1, ..., s∗
n) is
a Nash equilibrium if s∗
i is a best reply to s∗
−i for every player i ∈ N. (Maschler
et al., 2013, p. 96-97)
29. Chapter 4
Equilibrium Refinements
T
he Nash equilibrium is the most important solution concept in
game theory, but often games have more than just one Nash equi-
librium. In those games the intention is to find out which equilibria
are more reasonable than others. In this chapter, some equilibrium re-
finements will be introduced presenting solution concepts which disclose
differences between Nash equilibria.
One of the solution concepts for extensive-form games is the subgame
perfect equilibrium, which will be explained in Section 4.2. The idea behind
this method is to find non-credible threats.1 This equilibrium can be found
using backward induction.
4.1 Backward Induction
The following two sections are based on (Fudenberg & Tirole, 1991, p.
93-94) and (Watson, 2013, p. 186-89). Selten (1965) was the first who
argued that some equilibria are "more reasonable" than others. Figure 10
is a finite game of perfect information. The backward induction procedure
requires analysing a game from the leaves to the root. At the last decision
node in the game, the tourist needs to decide which of his strategy is best
1These threats are non-credible because their goal is to deter deviations by using
"irrational" behaviour off the equilibrium path.
15
30. 16 CHAPTER 4. EQUILIBRIUM REFINEMENTS
for him at this point downwards. He will choose "Go in" which reduces
the game for the seller to the same size the tourist had. The seller now
can decide between a payoff of 2 for "Wait" and a payoff of 3 for "Lure",
since he can be sure to have an opponent2 who is rational and who will
definitely choose strategy "Go in". Using this method, it is easy to find one
of two Nash equilibria highlighted yellow in Figure 10’s strategic-form and
red in the extensive-form.3 The other Nash equilibrium is stable as well,
because if the seller chooses "Wait" in the first place, the tourist’s decision
node will never be reached and therefore he loses nothing by playing
strategy "Stay out". Nevertheless, in Selten’s opinion, this equilibrium is
suspect. If the tourist’s information set is reached, he should play "Go in"
and therefore he always should choose this strategy. As a consequence,
the seller could anticipate this behaviour and choose "Lure". This would
lead to a higher payoff for both players. This is the reason the equilibrium
(Wait, Stay out) is not "credible", because its foundation is an empty threat
by the tourist to play "Stay out", which he would never wish to carry out.
In conclusion, there is always a pure-strategy Nash equilibrium in a finite
game with perfect information, which can be found through backward
induction.
4.2 Subgame Perfect Equilibrium
In the last information set of the game illustrated in Figure 11, none of
the strategies are dominated for the tourist. Here it is not possible to use
backward induction. If only the game starting at node z is considered,
the game would be a zero-sum simultanious-move game with one unique
Nash equilibrium having expected payoffs of (0,0). Now the whole game
starting at node z can be consolidated and replaced by its expected payoff.
This reduces the tree to the one in Figure 10. Players do not always select
their best responses ex ante. They make a rational decision when it is their
2The word opponent is often used to describe other players, but there are games
requiring cooperative behaviour where this terminology is not appropriate.
3The red path is also called the equilibrium path.
31. 4.2. SUBGAME PERFECT EQUILIBRIUM 17
Seller
(2, 0)
Wait
Tourist
(3, 1)
Go in
(0, 0)
Stay out
Lure
Seller
Tourist
Go in Stay out
Wait (2,0) (2,0)
Lure (3,1) (0,0)
Figure 10: Non-credible Nash equilibrium
move to take action. This is called sequential rationality.
Definition 6 [SEQUENTIAL RATIONALITY]: An optimal strategy for a
player should maximize his or her expected payoff, condidtional on every infor-
mation set at which this player has the move. That is, player i’s strategy should
specify an optimal action from each of player i’s information sets, even those that
player i does not believe (ex ante) will be reached in the game.
The logic behind subgame perfection is exactly that: Replace any proper
subgame4 by one of its Nash equilibrium payoffs and replace it in the tree.
After that, execute backward induction on the reduced tree.
Definition 7 [SUBGAME]: Given an extensive-form game, a node x in the
tree is said to initiate a subgame if neither x nor any of its successors are in an
information set that contains nodes that are not successors of x. A subgame is
the tree structure defined by such node x and its successors.
Considering Definition 7 the game trees below the nodes x, y and z can be
identified as subgames, but not below α.
4Subgames that do not start from the root are called proper subgames.
32. 18 CHAPTER 4. EQUILIBRIUM REFINEMENTS
Seller
x
(2, 0)
Wait
Tourist
y
(3, 1)
Go in
Seller
z
α
(2, −2)
C
(−2, 2)
D
A
α
(−2, 2)
C
(2, −2)
D
B
Stay out
Lure
Tourist
Figure 11: Subgame perfect Nash equilibrium
Definition 8 [SUBGAME PERFECT NASH EQUILIBRIUM]: A strategy
profile is called a subgame perfect Nash equilibrium (SPE) if it specifies a
Nash equilibrium in every subgame of the original game.
According to Definition 8, it can be stated that if the whole game is its
only subgame, the sets of Nash equilibria and SPE will coincide, but if
there is more than one subgame, some Nash equilibria may fail to meet
the criteria of a SPE.
33. Chapter 5
Games with Incomplete
Information
T
his chapter will focus on games with incomplete information introduc-
ing the concepts of beliefs and knowledge. A game with incomplete
information is a game where players do not have complete infor-
mation about the game. They may not know other players’ payoffs. For
instance, a seller does not know how much a potential customer values an
item and the customer probably does not know how much an item costs
to produce or how much rent the vendor pays for his shop. The same
situation does apply for games where dice are involved. In order to model
such games, information about the players’ beliefs and their knowledge
with the whole hierarchy of knowledge is needed.1 John Harsanyi’s inno-
vation (1967) of introducing a fictional new player to the game resulted
in the possibility to transform games with incomplete information to a
game with imperfect information. (Williams, (2013), p. 169; Maschler et
al., (2013), p. 319)
1It is necessay to have information about every player’s knowledge of the knowledge
of other players, knowledge of the knowledge of the other player’s knowledge of other
players, and so on.
19
34. 20 CHAPTER 5. GAMES WITH INCOMPLETE INFORMATION
5.1 Belief, Knowledge and
Sequential Equilibrium
This section concentrates on another equilibrium concept for extensive-
form games. Other than the subgame perfect equilibrium concept, where
it can be determined if a player’s action is rational for every subgame, this
concepts focus on games where such an approach is not possible. In many
games, players do not exactly know in which particular vertex they are
located. It is likely that the whole game is one big subgame and there
are no other subgames than the game itself. In such games, the players
need to form beliefs on how probable it is to be located at one node in
an information set and how strategies based on these beliefs will affect
the rest of the game. In this kind of games where a player is confronted
with multiple nodes in one information set, a player’s beliefs are specified
as a probability distribution p (0 ≤ p ≤ 1) over nodes in the information
set, which define how probable it is to have reached that specific node.
Based on the probability distribution p, a player must choose a sequentially
rational strategy. This means that given some beliefs, a player must choose
the strategy which gives him the highest expected payoff. (Williams, 2013,
p.170-171) (Maschler et al., 2013, p. 271)
Consider Figure 12 in which the seller does not know what kind of
tourist he is dealing with. The seller assumes that every tourist who
enters his shop has a 70 percent probability of being eager to buy. To act
sequentially rational, a player must maximise his expected payoff at each
information set. (Williams, 2013, p.171)
For instance, the tourist in Figure 12 should always choose "Buy" in his
information set on the left hand side, because "Not" is dominated by "Buy".
The seller knows this and would thereby choose action "High" at his left
vertex, which he reaches with probability p = 0.7. On the right hand side,
it may seem like the tourist should choose strategy "Buy’" when the game
reaches his decision set, but given his beliefs it is better for him to do
the opposite. In fact, by looking closer it can be observed that strategy
35. 5.1. BELIEF, KNOWLEDGE AND SEQUENTIAL EQUILIBRIUM 21
Nature
(10, 10)
Buy
(0, 0)
Not
High
(5, 20)
Buy
(0, 0)
Not
Low
p = 0.7 eager to buy
(10, −5)
Buy’
(0, 0)
Not’
High
(5, 10)
Buy’
(0, 0)
Not’
Low
p = 0.3 Not
Seller
Tourist Tourist
Figure 12: Sequential rationality
"High" weakly dominates strategy "Low". Looking at Figure 12’s strategic-
form in Figure 13, where the expected payoffs are already calculated, his
best strategy is visibly revealed. Considering the strategy profile (High,
BuyBuy’), with probability 0.7 there is (High, Buy) on the left hand side
and with probability 0.3 (High, Buy’) on the right hand side. This equals
in an ex ante expected payoff of 0.7 × 10 + 0.3 × 10 = 10 for the seller and
0.7 × 10 + 0.3 × (−5) = 5.5 for the tourist.
Seller
Tourist
Buy Not
High (10,10) (0,0)
Low (5,20) (0,0)
Seller
Tourist
Buy’ Not’
High (10,-5) (0,0)
Low (5,10) (0,0)
Seller
Tourist
BuyBuy’ BuyNot’ NotBuy’ NotNot’
High (10,5.5) (7,7) (3,1.5) (0,0)
Low (5,17) (3.5,14) (1.5,3) (0,0)
Figure 13: Strategic-form of Figure 12
36. 22 CHAPTER 5. GAMES WITH INCOMPLETE INFORMATION
5.2 Bayesian Nash Equilibrium
To form a Bayesian Nash equilibirum, which is the Nash equilibrium of a
game with incomplete information, a strategy profile and a set of beliefs
for every player is always necessary. The players are not only required to
choose credible strategies, but to hold reasonable beliefs. The Bayesian
equilibrium, which is a generalisation of a sequential equilibrium differs
only in the way how beliefs are modelled. A Bayesian equilibrium must
assume a weak consistency of beliefs. This means that for every information
set in the game which is reached with a positive probability, beliefs are
defined by Bayes’ rule. Information sets which are reached with positive
probability are on the equilibrium path, if its probability is 0, it is off the
equilibrium path. (Kreps and Wilson, (1982); Fudenberg and Tirole, (1991),
p. 209-215)
Definition 9 "A Static Bayesian Game consists of:
• The set of players I.
• For each player i:
– a set of possible types Ti
– set of actions Ai
• Payoffs which depend on the actions taken by all players and types:
∀i ∈ I, ui : A × T → R
• Probability measure on types p : T → [0, 1]
• All these elements are common knowledge." (Sáez Martí, 2015b)
Figure 14 will be used to explain Bayes’ rule. Imagine a tourist shows
interest in a product 60 percent of the time and a seller is able to observe
that. Thus, the seller will mention a higher price for that product 90
percent of the time. The seller’s behaviour is fundamentally subordinate
to the tourist’s interest. The probabilities on the different leaves are
based on prior beliefs. For instance, if the seller realises that the tourist is
37. 5.2. BAYESIAN NASH EQUILIBRIUM 23
interested, he will offer a high price, producing a conditional probability of
Pr(I0 | H1). This conditional probability is also called posterior probability
and is equal to:
Pr(I0 | H1) = I0∩H1
Pr(H1)
, Pr(H1) > 0, (1)
where I0 ∩ H1 is the probability that A and B both happen. The equation
above can be transformed into
Pr(I0 | H1) = Pr(I0 | H1)Pr(H1) = Pr(H1 | I0)Pr(I0)
Pr(I0 | H1) =
Pr(H1 | I0)Pr(I0)
Pr(H1)
=
Pr(H1 | I0)Pr(I0)
Pr(H1 | I0)Pr(I0) + Pr(H1 | U0)Pr(U0)
,
(2)
which is called the Bayes’ rule. (Williams, 2013, p. 188-189)
Definition 10 [BAYESIAN NASH EQUILIBRIUM]: In a static Bayesian
Game the stratgies s∗ = (s∗
1, ..., s∗
n) form a (pure-) strategy Bayesian Nash
equilibrium if for each player i and for each of i s types ti ∈ Ti, no player wants
to change his strategy, even if the change involves only one action by one type.
(Sáez Martí, 2015b)
39. Chapter 6
Cooperative Bargaining
A
ll previous chapters were presented to introduce the reader
to basic principles of game theory and to give the necessary
knowledge to understand the following chapters which build the
core of the research conducted. There is an immense amount of literature
based on the topic of bargaining published in the last decade. Most of it
concentrates on extensive-form games that represent important aspects of
trading. Thus, there is a growing number of individuals who think critical
about game theoretic predictions, because these cannot be used in general
for economic theory. Nevertheless, the importance of studying bargaining
in real-world settings has become well recognised and is taught by major
business schools. In this chapter, bilateral bargaining theory will be
presented, which models situations in which two players negotiate toward
an agreed-upon outcome. All bargaining games have two characteristics
in common. On one hand, the total payoff they could reach by achieving
an agreement is bigger than the payoff they could gain separately. On
the other hand, the negotiation is about how the existing surplus should
be divided. Each bargainer tries to get the most out of the negotiation
for himself, while facing the threat of ending up with no surplus if an
agreement fails. This threat causes bargaining to be a very strategic
matter. First, basic definitions and concepts of bargaining games will be
determined to then focus on the cooperative Nash bargaining solution and
25
40. 26 CHAPTER 6. COOPERATIVE BARGAINING
its properties. This solution concept is a function that assigns an outcome
to every game that one could think of as a recommended outcome by an
arbitrator or judge. (Dixit et al., (2015), p. 663-64; Chatterjee, (2014), p.
190)
6.1 The model
The following model of bilateral bargaining games1 with N = (1, 2) was
first presented and studied by Nash (1950) using a set S ⊆ R2 and a vector
d = (d1, d2) ∈ R2. The players try to reach an unanimous agreement
on some possible bargaining outcome x = (x1, x2) ∈ S. The outcome is
expressed as units of utility and in our examples as units of money, where
xi is player i’s utility from the outcome. The set S represents all possible
bargaining outcomes and the disagreement outcome or disagreement point2
d results if no agreement is achieved from the bargaining process. Each
player i has a preference ordering i over the set of lotteries over S ∪ {D}.
Note that it is assumed that bargainers satisfy the von Neumann and
Morgenstern assumptions.3 (Maschler et al., (2013), p. 622; Sáez Martí,
(2015a))
Definition 11 A [BARGAINING GAME] for N is a pair (S,d) where
• S is a nonempty, compact, and convex subset of RN,
• d ∈ S,
• There exitsts an alternative x = (x1, x2) ∈ S satisfying x d.
• The set of all bargaining problems is denoted by B.
• The function f : B → R2 assigns to each bargainin problem (S,d) a unique
element in S.
1It will be exclusively focused on games with two players but the reader should be
aware of games with multiple players.
2It is also called BATNA (best alternative of a negotiated agreement by the Harvard
Negotiation Project (Dixit et al., 2015, p. 666))
3The four axioms are completeness, transitivity, continuity, and independence.
41. 6.2. NASH BARGAINING 27
(Peters, (1992), p. 2; Maschler et al., (2013), p. 625)
6.2 Nash Bargaining
6.2.1 Nash Axioms
This section, which is based on (Napel, 2002, p.12), (Maschler et al., 2013, p.
627-30) and (Muthoo, 1999, p. 31-32), presents the four axioms which were
first proposed by Nash (1953). These axioms are mathematical expressions,
which should be used to find a bargaining agreement. The unique solution
concept presented in the next section satisfies these properties.
Invariance to Equivalent Utility Representations (INV)
Two bargaining problems (S, d), (S , d ) ∈ B should deliver the same
solution, if their utilities are changed according to positive affine trans-
formations. For instance, whenever τ(u) = αxi + β for constants α, β ∈ R
and α > 0, then
Axiom 1 f (τ(S), τ(d)) = τ(f (S, d)).
This is equivalent to a change of units from dollars to cents. It is reasonable
to require that a different representation should not change the solution.
Thus, although the bargaining solution of these two problems differ, they
must be related in the specified way.
Pareto Efficiency (PAR)
The second Axiom implies that a bargaining agreement is reached. The
goal is to get the best possible outcome for the players. Therefore, an
alternative solution cannot exist, where one player gets a higher output
without decreasing the other player’s outcome.4
4This stands for Pareto efficiency, named after the Italian economist Vilfredo Pareto
(1848-1923). In his book Manuale di Economia Politica he developed the idea that the
distribution of resources is not optimal if it is possible to increase at least one person’s
welfare without harming the interests of any other individual.
42. 28 CHAPTER 6. COOPERATIVE BARGAINING
Axiom 2 We fix (S, d) ∈ B and a bargaining solution f : B → R2. To have
Pareto efficiency there does not exist any utility pair (x1, x2) ∈ S ∪ {d}, such
that xi > fi(S, d).
Symmetrie (SYM)
A bargaining game (S, d) ∈ B is symmetric if d1 = d2, and (x1, x2) ∈ S if
and only if (x2, x1) ∈ S. If this is the case, then both players should be
treated equally.
Axiom 3 f1(S, d) = f2(S, d)
Indipendence of Irrelevant Alternatives (IIA)
The last axiom declares that options which are not selected should not
change the solution when they are removed. For every bargaining game
f (S, d) ∈ S and every subset S ⊆ T,
Axiom 4 f (T, d) ∈ S → f (S.d) = f (T, d).
6.2.2 The Nash Bargaining Solution
The four axioms showed above lead to the Nash bargaining solution.
Theorem 1 There is a unique bargaining solution concept N for the family
B → R2 satisfying INV, PAR, SYM and IIA. It is given by
f N(S, d) = arg max
x∈S,x≥d
(x1 − d1)(x2 − d2). (3)
Considering Figure 15, the solution N (S, d) maximises the area of the
rectangle with bottom left vertex d and top right vertex x. N (S, d) is
the Nash bargaining solution5 of the bargaining game (S, d). For every
point x ∈ S with x ≥ d, the area of the rectangle is the product of
f (x) = (x1 − d1)(x2 − d2) which is called the Nash product. (Maschler et
al., 2013, p.630-31)
5It is also called the Nash agreement point.
43. 6.2. NASH BARGAINING 29
N (S, d)S
d
Figure 15: The Nash bargaining solution
Imagine a family in their holidays in Turkey. This family has two
children, Sebastian and Doreen. Their father offers them 100 dollars for
shopping, if they can achieve an agreement on how to split this amount
between each other. If no agreement is reached, Sebastian and his sister
will both get 25 dollars each. 25 + 25 < 100, so there is clearly a surplus
from agreement. If this was not the case, both, Sebastian and Doreen,
would take their outside opportunities and no bargaining would take place.
When there is a surplus, consider the rule: each of the two children is
given his disagreement outcome plus a share of the surplus. This share is
depending on their relative bargaining strengths, which will be discussed
later in this chapter. Considering Axiom 3, the share must be 1
2 each to
achieve symmetry. Using equation 3 of the Nash bargaining solution, the
result is:
arg max
x1
(x1 − d1)((100 − x1) − d2) = arg max
x1
(x1 − 25)((100 − x1) − 25)
FOC : x1 = 50 → x2 = 50
f N
(S, d) = (50, 50)
(4)
A geometric representation of the Nash solution is shown in Figure 16.
The disagreement point is in d, all points (x1, x2) on the blue line divide
the gains in proportions 1/2
1/2 = 1
1 between Sebastian and Doreen and all
points on the line from (0,100) to (100,0) use up the whole surplus. The
44. 30 CHAPTER 6. COOPERATIVE BARGAINING
slope = 1/2
1/2 = 1
x1 + x2 = 100
fN (S,d)
d
Figure 16: The Nash bargaining solution in a simple way
intersection between the blue and the black line is the Nash bargaining
solution (50,50). Modifying this example in a way in which the father does
not give both children the same amounts in case of disagreement, this
would move the blue line up or down without changing its slope. Note
that if one of the children is more risk averse6 the bargaining problem
changes and the less risk averse child gets a higher share. It is important
to be familiar with the cooperative Nash bargaining solution, but the
most important model to examine behaviour at the Grand Bazaar is the
non-cooperative model explained in the next chapter. (Dixit et al., 2015, p.
666-68)
6This would make his utility function more concave.
45. Chapter 7
Noncooperative Bargaining
T
his chapter will analyse the non-cooperative bargaining repre-
sented by extensive-form games, being the basis for explanation of
observed strategic behaviour at the Grand Bazaar. First, ultimatum
games will be introduced by using a basic example and then attention will
be aimed towards the non-cooperative Rubinstein’s basic alternating-offers
model. This model will build a basic framework which can be extended
and modified later on.
7.1 Ultimatum Games
The simplest of bargaining models is the ultimatum bargaining game. It
is a game where one player makes an offer and the other can accept or
reject. This is the whole game in which all bargaining power is on the
proposer’s side. Imagine a tourist at the Grand Bazaar likes one of the
paintings in one of the stores. This painting was already in the store when
the seller bought it from his predecessor and therefore has no value to him.
Since the painting is worth $100 for the tourist and nothing for the seller,
a trade would generate a surplus of $100. The price determines how this
surplus is divided between these two players. There is a unique subgame
perfect equilibrium in this game in which the tourist gets the painting for
free. This standard ultimatum game is pictured in Figure 17. Note that
31
46. 32 CHAPTER 7. NONCOOPERATIVE BARGAINING
Tourist
0
0
(1 − m, m)
Accept
(0, 0)
Reject
Seller 100
Figure 17: Ultimatum game
the tourist can make any offer between 0 and 100, and that the seller then
decides between the outcomes (100 − m, m) and (0, 0), where m stands for
the tourist’s offer. (Watson, 2013, p. 244-45)
By observing the game, one can recognise that this game has 100 ×
100 = 10 000 subgames. One subgame for every different amount the
tourist could offer to the seller. It seems obvious that the seller should
accept every offer m > 0. Only when m = 0, rejection could be a best
response for the seller. In a game like this, in which a smallest monetary
unit exists (1 cent), the subgame perfect equilibrium is where the tourist
offers the smallest possible amount and the seller accepts it (99.99, 0.01).1
The subgame perfect equilibrium is efficient, because the whole surplus is
shared between the players. (Watson, 2013, p. 245-46)
1Note that the unique subgame perfect equilibrium in a game without a smallest
monetary amount would be (100,0), respectively 0 for the responder and the whole
surplus for the proposer.
47. 7.2. RUBINSTEIN’S BASIC ALTERNATING-OFFERS MODEL 33
7.2 Rubinstein’s Basic Alternating-Offers Model
The ultimatum game is a too simplistic model for most real-world nego-
tiations. In reality, there are processes where players take turns to make
offers to each other until an agreement is reached. Rubinstein’s model
provides with several insights about bargaining situations. One insight
is that bargaining processes without any costs for haggling are indeter-
minate. Hence, not only players’ preferences, but also their combination
with agreement times are crucial elements for sequential bargaining. Cross
(1965, p.72) stated:
If it did not matter when people agreed, it would not matter whether
or not they agreed at all.
This is intuitive since most people are impatient to some degree and
do not prefer to bargain for too long. Additionally, most people discount
future payoffs relative to the present. In game theoretic models, the motion
of a discount factor δi ∈ (0, 1) is used. How someone discounts the future
and how impatient someone is, will affect the surplus each negotiator gets.
(Muthoo, (1999), p. 42; Watson, (2013), p. 246-47)
The bargaining procedure will now be specified before modifying the
previous ultimatum game to an alternating-offers game. Offers are made
in particular points of time. Player A offers at time t∆2 when t is even
(i.e., t = 2, 4, 6, ...) and Player B can accept or reject it. If he rejects, he can
make a counteroffer in (t + 1) and Player A can decide whether he wants
to accept or reject. If Player i accepts an offer for a share mi (0 ≤ mi ≤ π)
of the surplus, Player i’s payoff will be mi × δt. (Muthoo, (1999), p. 42-43;
Napel, (2002), p. 31)
Now consider the ultimatum game in Figure 17 to have two periods
with an additional discount factor for both players. Again, the tourist
makes the first offer and the seller can decide whether to accept or reject.
If he rejects he can make a counteroffer. In the second period one finds
2∆ stands for any possible time frame (e.g. hour, day, week). It shall be noted that for
simplicity and for the ease of reading, ∆ will not be used in following examples and will
be replaced by 1 instead.
48. 34 CHAPTER 7. NONCOOPERATIVE BARGAINING
himself back in an ultimatum game, but with reversed roles. The seller
has the bargaining power now. If an agreement is reached in the second
period, the payoffs are discounted relative to the first period. Therefore
the tourist would get m2δ1 and the seller (1 − m2)δ1. The extensive-form
is on the left and the bargaining including the disagreement point are
pictured on the right hand side. The outer line in the picture on the
right represents the payoff vectors they could reach if they come to an
agreement in the first period. The inner line represents the same for the
second period. It contains the discounted payoff vectors from the first
period. The subgame perfect equilibrium is easy to find in this example.
The solution for the ultimatum game in the second period was already
shown in the previous section. Discounting these payoffs results in 0.01δ1
and 99.99δ2 as continuation values. Therefore, the seller should reject any
offer m1 < 99.99δ2 and will be indifferent for m1 = 99.99δ2 but he will
definitely accept if the tourist offers an amount m1 ≥ δ2. This leads to the
unique Nash equilibrium of (1 − δ2, δ2). The right hand side of Figure 18
offers a graphical illustration of this equilibrium. (Watson, 2013, p. 247-50)
Expanding this bargaining model of alternating-offers to a finite num-
ber of periods T will not change anything in the solution finding process. It
can be analysed in the exact same way. For every even number of periods,
Player 2 will have the final offer and for every odd number, Player 1 will
have the last offer. In case of agreement in period t, the payoffs need to be
discounted by δt−1
i . Note that patience is positively related to bargaining
power. The closer a discount factor in Figure 18 gets to 0, the smaller a
player’s payoff gets. One of the most interesting parts of this model is that
modifying T does not change the fact that agreement is always reached in
the first period, where the biggest joint value is. (Watson, 2013, p. 249-50)
This game can also be expanded to infinite periods of T with the
difference that backward induction is no longer possible. At this point, it
is known that a subgame perfect equilibrium must satisfy the following
two properties:
Property 1 No Delay: Whenever a player has to make an offer, her equilibrium
offer is accepted by the other player.
49. 7.2. RUBINSTEIN’S BASIC ALTERNATING-OFFERS MODEL 35
Tourist
0
0
(1 − m1, m1)
Accept
Seller
0
0
(m2, 1 − m2)
Accept
(0, 0)
Reject
Tourist 100
Reject
Seller 100
u2
u1
d
100
δ1 100
δ2
1− δ2
Figure 18: A two-period game
50. 36 CHAPTER 7. NONCOOPERATIVE BARGAINING
Property 2 Stationarity: In equilibrium, a player makes the same offer when-
ever she has to make an offer.
(Muthoo, 1999, p.44)
Given Property 2, Player 1’s equilibrium offer should put Player 2 in
a position where he is indifferent between accepting and rejecting. Like
shown before, indifference means that δ2(1 − m1) = m2. This equation
holds for both players and therefore δ1(1 − m2) = m1. Solving these
equations results in
m1 = δ1(1−δ2)
1−δ1δ2
and m2 = δ2(1−δ1)
1−δ2δ1
. (5)
Given Property 1, an agreement must be reached in the first period which
leads to the unique subgame perfect equilibrium (x∗, y∗):
x∗(δ1, δ2) = 1−δ2
1−δ1δ2
and y∗(δ1, δ2) = δ1(1−δ2)
1−δ1δ2
(6)
(Muthoo, (1999), p. 43-45; Napel, (2002), p. 38-39)
7.3 Asymmetric Information
In real bargaining situations at the Grand Bazaar at least one of the ne-
gotiators has some relevant information which the other does not have.
There are in general a variety of things that may be relevant to the bargain-
ing outcome. The payoffs depend on players’ private information about
their preferences and their reservation values.3 In this section, the role of
asymmetric information on the bargaining outcome is studied, at which at
least on of the player’s reservation values is his private information. The
focus lies on a bargaining situation in which a seller owns an object that a
tourist wants to buy. If an agreement is reached at a price p (p ≥ 0), the
seller’s payoff will be p − c and the tourist’s payoff v − p, where c denotes
3The maximum price at which a buyer is willing to buy and the minimum price at
which a seller is willing to sell.
51. 7.3. ASYMMETRIC INFORMATION 37
the seller’s reservation value4 and v denotes the tourist’s reservation value.
In case of disagreement both players’ payoff is equal to zero.5 (Muthoo,
1999, p. 251-53)
7.3.1 One-Sided Uncertainty
In this section, it is assumed that only one side has private information
about their reservation value and that reservation values of the players
are independent. This scenario is closer to reality, where an informed
buyer could have information about production costs of offered goods and
also about costs for rent which could reveal a seller’s reservation value.
Inversely, a seller with all his experience also might have the ability to
get information on a buyer’s reservation value, before negotiations even
started. Furthermore, there is a possibility for both players to acquire in-
formation about their opponents’ reservation value during the bargaining
process. In contrast to the case where the player making offers has all
the bargaining power, Muthoo (1999) has proven that if the opponent has
private information, the payoffs of the offer-making player are adversely
affected. He also studied the existence of a screening equilibrium in which
the uninformed player gets information during the bargaining process
about his opponent’s reservation value.
Screening Equilibrium
In this section, the results of Muthoo (1999) are analysed presenting the
perfect Bayesian equilibrium (PBE) he found as a result. In order to do so,
an introduction to some variables is needed. Consider a situation where
player’s reservation values are independent and the seller’s reservation
value is his private information. Let G be the seller’s reservation value
which is uniformly distributed on the closed interval [0, 1]. The buyer be-
lieves that the seller’s reservation value is less than or equal to c. Therefore,
4The sum of his cost of production and other expenses like rent, electricity and water.
5The seller still has to pay for expenses like rent, but for simplicity this factor is
disregarded in one single bargaining process in a mass of many in one day.
52. 38 CHAPTER 7. NONCOOPERATIVE BARGAINING
G symbolises the buyer’s prior beliefs. G’s maximum and minimum value
are denoted by c and c, where c ≥ c ≥ 0. This leads to, G(c) = 1, G(c) = 0
if c ≤ c and G(c) ≥ 0 if c ≥ c. λ stands for the lowest value the buyer
thinks the seller could have. For this example let the buyer’s reservation
value be v = c. Muthoo came to the conclusion that there is a perfect
Bayesian equilibrium which is defined by the following two equations.
pn = 1 − (1 − β)βn and λn = a − βn (n = 0, 1, 2, ...) (7)
with
α = 1 −
√
1 − δ β = 1−
√
1−δ
δ 1 ≥ β ≥ α ≥ 0 (8)
Note that along the equilibrium path, the prices are strictly increasing and
agreement will be reached with probability 1. The higher a seller’s cost
of production the more periods it takes until agreement is reached. The
seller’s private information is in fact (partly) revealed during the bargain-
ing process. This process resembles to an intertemporal price discrimination.
Nevertheless, the equilibrium is inefficient since trade does occur with
positive probability after period 0. The bigger the discount factor gets,
the higher the probability of offering a high enough price for the seller to
accept the first offer is. Furthermore, the buyer’s payoff gets closer to zero.
However, for the research at the Grand Bazaar a small discount factor is
more realistic, thus screening for privately held information is possible.
Muthoo also proved that there is a continuum of PBE if v = c like in the
example above, but there is a unique PBE if v > c and gains from trade
exist with probability 1. (Muthoo, 1999, p. 272-82)
The No Gap Case
For the research at the Grand Bazaar one particular modification may
be important. When the time interval between two consecutive offers is
arbitrarily small, the following theorem provides with a characterisation
of the set of buyer payoffs sustainable as a PBE.
53. 7.3. ASYMMETRIC INFORMATION 39
Theorem 2 Assume that v = c, and that G is continuously distributed on the
closed interval [c, c]. Let ˆuB be such that ˆuB ≥ (v − p)G(p) for all p ≥ 0.
For any > 0 there exists a ∆ > 0 such that for any ∆ ≤ ∆ and any
uB ∈ [ , ˆuB − ] there exists a PBE such that the buyer’s payoff equals to uB.
This means that there exists a PBE in which an uninformed buyer could
still get arbitrarily close to a payoff of ˆuB if the time interval is arbitrarily
close. (Muthoo, 1999, p. 284-85)
7.3.2 Two-Sided Uncertainty
Chatterjee and Samuelson (1987) proved that there is a unique Nash
equilibrium in a situation with two-sided uncertainty. The model is
characterised by the following:
Valuation Discount factor
Type Seller Buyer Seller Buyer
Hard s b Ds Db
Soft s b Ds Db
where s ≤ b < s ≤ b and discount factors were drawn from the interval
(0,1). They let
π1
s be the initial probability that a seller o f unknown type is so f t and
π1
b be the initial probability that a buyer o f unknown type is so f t
They first studied a model with two types of buyers and sellers in which
they could be strong or weak and then expanded to a model in which
the buyers and sellers could be any kind out of a continuum of types.
Nevertheless, the extended model behaved similar to the first one which
led to following results:
Theorem 3 Any of the potential gains s − b which are realized in the bargaining
process accrue either entirely to the seller or entirely to the buyer. The buyer is
more likely to receive these gains from trade if i π1
s is relatively large; π1
b small;
54. 40 CHAPTER 7. NONCOOPERATIVE BARGAINING
πs small and πb large (equivalently [...] Ds small; Db large; b − s small and
b − s large (given s − b)). The seller is more likely to receive the gains from trade
under opposite conditions.
(Chatterjee & Samuelson, 1987, p. 187)
7.4 Other Modifications
The following three sections are based on (Muthoo, 1999, p. 73-74, 99-100,
137-38)
7.4.1 Risk of Breakdown
There is a possibility that negotiations break down in a random manner.
However, the risk of an "intervention" by a third party is negligibly small
at the Grand Bazaar. The possibility that another seller could cause
negotiations to break down is almost zero, because norms and manners
do not allow such a behaviour. The risk of having a potential buyer in
company of his wife or children who could cause negotiations to break
down, for reasons like a sudden discovery of something interesting in
an other store, is also negligible considering that bargaining process are
generally short at the Bazaar. This leads to the cognition that the risk of
breakdown can be disregarded in this thesis. (Küçükerman & Mortan, 2007,
p. 70-71)
7.4.2 Outside Options
Imagine a tourist shopping at the Grand Bazaar. He suddenly finds a
nice piece of clothing at the first store he walks in. After negotiation, he
and the seller reach an agreement on the price. The tourist then decides
to look around in the Bazaar first and in case he cannot find something
similar which gives him the same value for a cheaper price, come back to
the first store and buy the piece for the agreed price. There are models
which study the impact of such an outside option on further negotiations in
55. 7.5. REPUTATION EFFECTS 41
other stores. Nevertheless, for this study of the Grand Bazaar, this kind of
modifications of the alternating-offers model can be ignored. The tourist
in this example can never be sure to find this piece he liked when he
returns to the first store. The seller could have sold it by then. There is also
a possibility of the seller recognising the returning tourist and realising
that he could not find a better offer which in the worst case could result
in increasing prices. It is also highly unlikely that a seller has an outside
option like this, since he would sell his goods for an acceptable price and
would not have the opportunity of waiting for a better paying customer
while letting the first one wait.
7.4.3 Inside Options
Models with inside options contain bargaining over an indivisible good
which has a utility to his owner in each period. For instance, if a seller
and a buyer bargain over the price of a house, the seller still gets a utility
of living in this house in each period as long as the bargaining goes on.
Inside options are also not applicable for the Grand Bazaar, because sellers
cannot gain a utility from their goods like in the example before. Even if
some of them could, like the jewellers who could wear their accessories
themselves, cleaning them afterwards would erase the gained utility right
away. On the contrary, if there is an inside option for sellers it would be
negatively correlated to their payoff, because they still have to pay the rent
for their stores in case of disagreement. The buyers may have an inside
option in the interest they get from their banks for keeping their money in
their accounts, but the amount of interest they will get during the short
period of negotiation at the Grand Bazaar is also negligible.
7.5 Reputation Effects
There are many tourists at the Grand Bazaar of Istanbul, but there are quite
a lot of local customers too. The difference to the foreign customers is that
some of the locals are sent to a store by recommendation or they know
56. 42 CHAPTER 7. NONCOOPERATIVE BARGAINING
the seller from previous transactions. In cases like these, the bargaining
situation changes. The seller and the buyer find themselves in a repeated
bargaining game. The seller could try to build a reputation of having a
good price-quality ratio. This could lead to potential new customers by
recommendation and returning previous customers. Thereby, the seller
should intuitively agree on lower prices to bind his customer and get
a benefit from future transactions.6 How much lower the price will be
relative to the single-shot bargaining game, is dependent on the time
intervals between transactions and the buyer’s ability to assure the seller
of future transactions. (Fudenberg and Tirole, (1991), p. 416-21; Muthoo,
(1999), p. 295-315)
6The idea behind it is that it is better to get 10 times a payoff of 1 than a payoff of 5
once.
57. Chapter 8
The Grand Bazaar of Istanbul
T
he Grand Bazaar1 of Istanbul is one of the largest and oldest bazaars
in the world. It is located in the heart of Istanbul and can easily
be reached by public transportation. It has 8 main entrances, 65
streets on an area of 40 000m2 and 3300 stores with 40’000 employees. It
attracts up to 300’000 visitors a day and is therefore one of the most-visited
tourist attractions worldwide.2 Although there are items sold coming out
of serial production, the Bazaar still has some interesting, antique and
unique goods to offer. This and its incomparable atmosphere still drives
foreign and local visitors to the bazaar, looking for something to haggle
about while drinking traditional Turkish tea. (Küçükerman & Mortan,
2007, p. 251)
1Its Turkish name is Kapalıçar¸sı which means "Covered Market".
2This data was published by the Turkish Ministry of Culture and Tourism
in 2007 and the same information can be found on their official website
(http://www.kultur.gov.tr/EN,113801/grand-bazaar.html), however the Grand Bazaars
official website (http://www.grandbazaaristanbul.org/The_Grand_Bazaar.html) claims
that there are 5000 shops and up to 400’000 visitors daily. Thus, a representative of the
Association of Merchants at the Grand Bazaar claimed that there are approximately 3520
stores.
43
58. 44 CHAPTER 8. THE GRAND BAZAAR OF ISTANBUL
8.1 History
Mehmed the conqueror, who was an Ottoman sultan and ruled from
1444 to 1446 and from 1451 to 1481, gave the order to build the Cevahir
Bedesten (Bedesten of gems) in winter 1455/56. The construction of this
building which today forms the core of the Grand Bazaar, ended in winter
1461/62. Although the architecture is purely Ottoman, there is a relief
of a Byzantine eagle on top of the East Gate, which always gave space
for interpretation whether or not the building could have been Byzantine
beforehand. Despite some fires during its history, the stores in the Cevahir
Bedesten are still built out of wood. Only the most valuable goods were
traded in this Bedesten because it was possible to lock the Bedesten and
the stores were only open at certain times a day. (Küçükerman & Mortan,
2007, p. 162)
The first fire happened in 1515 and shortly after, a second covered
market called the Sandal Bedesten was built from 1545 to 1550. This led
to a movement of textiles to the Grand Bazaar. Soon a lot of businesses
surrounded both markets and finally the gap between them was closed.
The Grand Bazaar reached its final shape in the beginning of the 17th
century. The concentration of commerce to this area caused recurring fires
throughout the history of the Grand Bazaar.3 In 18th century, after the big
fire of 1730, Ibrahim Pasa4 decided to renew the burnt areas of the Grand
Bazaar and to change the wood in the stores to masonry. He also decided
to cover several markets between the Bedestens with vaults. (Küçükerman
& Mortan, 2007, p. 162)
The Grand Bazaar was an exceptional and incomparable market until
the first half of the 19th century. The beginning of industrial revolution in
Great Britain and the newly discovered possibilities of mass production in
the textile industry caused a decline for the prosperous market’s economy.
(Küçükerman & Mortan, 2007, p. 172-215)
3In the years 1548, 1588, 1618, 1645, 4658, 1660, 1687, 1688, 1730, 1750, 1766, 1791, 1943
and 1954 are documented fires.
4He was the first Grand Vizier of the Ottoman Empire appointed by Sultan Suleiman
the Magnificent.
59. 8.1. HISTORY 45
In 1894, a strong earthquake shattered Istanbul. The Bazaar took
big damage and as a consequence one of the most important markets,
the second-hand Bazaar, became an open-sky road. In 1914, the city of
Istanbul bought the Sandal Bedesten and turned it into an auction house
for carpets, due to a situation of devastation of the merchants of textile
goods. (Küçükerman & Mortan, 2007, p. 162, 222-24, 238-39)
Figure 19: Life at the Grand Bazaar in the 19th century
(Küçükerman & Mortan, 2007, p. 217)
60. 46 CHAPTER 8. THE GRAND BAZAAR OF ISTANBUL
8.2 Merchants at the Grand Bazaar
The merchants at the Grand Bazaar were sitting along both sides on
wooden divans in front of their stores. A potential customer could sit next
to the seller and talk together while drinking tea or Turkish coffee with
him. There are still some merchants sitting in front of their stores and
holding up the tradition. However, back in time the atmosphere was more
relaxed, whereas nowadays the rush of modern civilisation found its way
into the Bazaar. Until the restoration following the earthquake of 1894,
the merchants of one good were compulsorily concentrated on one street
which got its name by the merchants’ professions. The Cevahir Bedesten
hosted jewellers, armourers and crystal dealers, while the Sandal Bedesten
was the center for textiles. This kind of separation did disappear partially,
but there is still a remarkable concentration of the same businesses along
certain roads. (Gülersoy, 1980, p. 18-34)
The ethics of the merchants changed drastically over time. Until the
first half of the 19th century the merchants were indifferent to profit, there
was no envy between the sellers and only one single and fair price was
offered to their customers. This behaviour was due to the ethics of Islam
and a social security system provided by the guilds. The guilds were
taking care of their members for a monthly fee. They lost importance
during the 19th century and were abolished in 1913. Since 1952, there exists
an Association of Merchants of the Grand Bazaar, although it does not
represent all of the merchants. Alongside with westernisation, mercantile
ethics found their way to Ottoman society and today’s merchants at the
Grand Bazaar are driven by profit in the same way Western traders are.
(Gülersoy, 1980, p. 43-48) (The official Grand Bazaar website, 2016)
61. Chapter 9
The Field Research
The goal of the research at the Grand Bazaar was to study bargaining
behaviour of its merchants. The most obvious path would have been to
observe as many as possible bargaining situations and concentrate on some
specific details. However, an approach like this was not possible during
the time this research was conducted. It was off-season in February and
Istanbul was target of terrorist attacks the months before, which caused
many tourists to stay away from Istanbul and its crowded places. The
sellers claimed that this was the worst February since 30 years. Besides,
sellers preferred their stores to be empty while potential customers were
around. They tried to avoid any distraction which meant that observation
was not possible.
9.1 Questionnaire and Conduction
Therefore, another approach was followed which took advantage of the
current situation. A questionnaire was created which intended to acquire
knowledge about the influence of a buyers’ characteristics on the price
setting of the sellers. The goal was to collect information about sellers’
behaviour regarding possible disclosure of buyers’ reservation values.
47
62. 48 CHAPTER 9. THE FIELD RESEARCH
In the first question of the questionnaire, the sellers were asked to
scale the following attributes’ importance from 1 to 10. 1 = (absolutely
unimportant) and 10 = (extremely important) indicated the importance in
regards to the price setting.
• Age
• Nationality
• Gender
• Interest in product
• Wearing apparel
• Accent
• Sympathy
• Number of articles
• Time
• Date
• Receipt
• Cash
Additionally, at the end of this section, some empty rows were added.
The merchants had the possibility to add some uncovered characteristics
which were not included in this list. It must be noted that "receipt" and
"cash" are different from the other attributes. Those are characteristics
which a buyer can add to his profile during negotiations. It does not reveal
information about his reservation value, thus it may have influence on the
price.
The second section of the questionnaire put focus on the relation of
characteristics to a difference in price settings. Knowing that the time of
the day is relevant to a seller’s price setting is not sufficient. It is important
to know if it affects it positively or negatively for the customer. The sellers
were asked to mark each of the following statements with the number
which describes best how they feel about it from 1 to 5, with: 1 = strongly
disagree, 2 = disagree, 3 = neither agree nor disagree, 4 = agree and 5 =
strongly agree.
63. 9.1. QUESTIONNAIRE AND CONDUCTION 49
• The older the customer is, the
lower the price gets.
• A foreign customer gets a
higher price than a local.
• A female customer gets a
higher price than a male.
• The more interest a customer
shows in a product, the higher
the price gets.
• The better dressed a customer
is, the higher the price gets.
• The better a customer’s Turk-
ish is, the lower the price gets.
• The friendlier a customer is,
the lower the price gets.
• The more articles a customer
wants to buy, the lower the
price gets.
• The later the time of the day is,
the lower the price gets.
• The price is lower off-season.
• The price is lower if the cus-
tomer pays in cash.
The third section of the questionnaire examines the sellers’ price ranges.
They were asked to declare how much profit they make from one item
at least, which was equivalent to their reservation value. Another goal
was to gain insights into how much profit they make at most. These two
pieces of information defined an interval of possible points of agreement
a particular seller had reached with different customers. The third part
of this question asked how much they were willing to decrease the initial
price they had set during negotiations. The information gained from
this question could indicate the importance of an initial price setting and
therefore, how important it is for a potential customer not to reveal any
information about their reservation values.
In the forth section of the questionnaire, the sellers were asked to
disclose some private information for statistical purposes:
- their age.
- their gender.
- what kind of product they sell.
- how many years of experience
they have.
- whether or not they own the
store they are working in.
64. 50 CHAPTER 9. THE FIELD RESEARCH
Conducting the survey alone resulted in moderate success. The mer-
chants were not willing to take part in a survey like that with a person
they did not know and from whom they could not expect to get something
in return. Numan Hocaosmano˘glu, a member of the Istanbul Chamber
of Commerce, involved two of his colleagues, Ilhami Yazıcı1 and Mustafa
¸Senocak2 into the research. Both of them had an immense amount of
influence in the Grand Bazaar. With their help, assistance by either a
known member of the Association of Merchants at the Grand Bazaar (Ilker
Yılmaz) or a police officer (Mehmet Yıldız) was provided to conduct the
survey. This eased the contact to the merchants and consequently the
surveying process immeasurably.
Thanks to Ilker Yılmaz, actual information about the distribution of
the different sellers in the Bazaar was gained. This enabled the possibility
to concentrate on surveying at least 5 percent of all merchants of each
different sector to achieve statistically significant results. 57 jewellers3, 19
carpet dealers, 27 textile dealers, 26 leather dealers and 47 sellers of gifts
were interviewed, resulting in a total number of 176 conducted surveys.
9.2 Results
The programming language R and an integrated development environ-
ment called R-Studio was used for the evaluation of the data. Snippets
of the R-code can be found in the appendix. Having a data matrix with
177 observations and 31 parameters, the analysis of the data was started
by clustering the sellers into different groups. First, they were clustered
into the groups of the goods they were selling and then differentiated by
shop owners and employees to encounter possible differences between the
1Member of the Board of Directors of the Association of Merchants at the Grand Bazaar
and Founder and CEO of the Yazıcı Group, one of the biggest enterprises in the gold
market with a revenue of 600 millions Turkish Lira. (www.ito.org.tr/wps/portal/gazete-
detay?WCM_GLOBAL_CONTEXT=ito_portal_tr/ito-portal/gazete/gzt-2014/gzt-2014-
9/gzt-2014-9-26/edd1de004608108898a9bb6b36283c4f)
2President of Leather and Leather Products Exporters’ Union
3Combines gold, silver and copper sellers.
65. 9.2. RESULTS 51
Table 1: Size of clusters
Groups Number Groups Number
Jewellery sellers (J) 57 J ∩ O 18
Carpet sellers (C) 19 J ∩ E 39
Textile sellers (T) 27 C ∩ O 8
Leather sellers (L) 26 C ∩ E 11
Gift sellers (G) 47 T ∩ O 13
Shop owners (O) 75 T ∩ E 14
Employees (E) 101 L ∩ O 10
L ∩ E 16
G ∩ O 26
G ∩ E 21
groups. This clustering would possibly give some insights into how their
motivation could influence price settings (short term gains-employee vs.
long term gains-owner).
Histograms were created to analyse the data of the first section of the
questionnaire looking for certain trends. The results of this first step can
be separated in three groups. Characteristics which seem to be important,
those which seem to be unimportant and those who need a closer analysis
due to a high density of answers on both extremes. There was no buyer’s
attribute which seemed to be mediocre important for all respondents. The
peaks are always on the outer extremes, which was an expected result.
In the following sections different levels are referred to. The first level is
without clustering. In the second level the data is clustered into different
goods OR owners and employees and in the third level the data is clustered
into different goods AND owners and employees. All the histograms can
be found in the appendix.
At this point, it must be noted that there must be a reasonable amount
of doubt regarding the merchants’ answers to these questions. It is pos-
sible that some of them were not faithfully answering. They demanded
justification for the questions, explanation of motives and intentions with
66. 52 CHAPTER 9. THE FIELD RESEARCH
Table 2: Mean and standard deviation of the characteristics
Statistic N Mean Median St. Dev.
Influence of age 176 4.222 4.50 3.195
Influence of nationality 176 5.534 6.00 3.547
Influence of gender 176 3.551 1.00 3.122
Influence of interest for a product 176 6.080 7.00 3.678
Influence of wearing apparel 176 5.233 5.00 3.572
Influence of accent 176 3.869 3.00 3.169
Influence of sympathy 176 6.676 8.00 3.378
Influence of number of articles 176 7.250 8.00 2.877
Influence of time of the day 176 4.000 2.00 3.406
Influence of date 176 3.688 2.00 3.234
Influence of wanting a receipt 176 2.943 1.00 3.006
Influence of paying cash 176 5.205 5.00 3.656
the results. The merchants were clearly scared of people who could harm
them and their businesses. They were scared that the data could be sold to
travel agencies who would use the collected data for their customers. The
sellers stated that they are often confronted with tourists using modern
technologies in form of their smart phones to find out at which stores in
the Bazaar they can get the best prices. Apparently some tourists seem
to know exactly for what prices some previous goods were sold. This
aggravates the sellers’ negotiation by a remarkable amount. Therefore, the
following results should be kept in perspective.
Age
More than 63% of all merchants gave an answer of 5 or below at the first
section of the questionnaire and looking at its histogram, a clear peak at 1
is observable. Going one level deeper in which the results are clustered to
the different type of goods, a big difference is not noticeable. The results
do not change by clustering to owner and employee either. Only when
clustered one step further and looking at the data on a third level in which
the data for different goods are clustered again to owners and employees.
67. 9.2. RESULTS 53
It is observable that owners of leather stores and employees of textile
stores think that age can have an effect to the price. It must be noted that
this does not mean they think age has a big impact on the price, only that
in some cases it can be important. Gift shop employees did not agree with
each other either. Some of the merchants argued that they are aware of the
fact, that some young customers do not have the same amount of money
like adults do. Therefore, age can have an impact on the price settings.
One textile seller even remarked that some of the sellers at the Bazaar give
discounts to students.
Nationality
There was some dissent on this issue. The merchants were separated into
two groups. Almost 50% of the sellers answered with 5 or less. This
is clearly a characteristic which needs to be analysed on deeper levels.
On the second level, nationality seems to affect the price most for the
gift and leather sellers. It is also more important to employees than to
shop owners. On the third level, the results show that a foreign customer
should beware of textile and leather shop employees and also generally
in gift shops. The probably most remarkable result is concerning the
carpet store owners, whose majority thinks that nationality affects the
price a lot, but a big majority answered at the second section of the
questionnaire, that this does not mean automatically that the price rises
when a customer is foreign. Conversations with the sellers concluded that
they do differentiate between nationalities. Turkish customers are often
paying more for a carpet than foreigners. During the interviews with
the different sellers, it was remarkable how some of them were a little
offended and felt accused of being a hustler while others admitted openly
that they set a higher price for some foreign customers. These were mostly
younger sellers with less experience, who probably did care less about
reputation effects.
68. 54 CHAPTER 9. THE FIELD RESEARCH
Gender
A customer’s gender has the second lowest mean of all the surveyed
characteristics and the median is a straight 1. Over 73% of all respondents
rated it 5 or lower. There are no differences in the results on the second
level, and only the leather sellers who are also store owners delivered
uncertain results. This can be explained that a big part of their product
spectrum are leather purses and it seems obvious that men are not ready
to pay as much as women for those items. Only a lack of experience could
explain why their answers are such different from employees in the same
sector. However, some merchants regardless of their sector claimed that,
in general, women are better negotiators and often achieve to agree on
lower prices than men.
Showing Interest
This feature is clearly one of the most important. It has a high mean
and even a higher median. This makes intuitively sense since being very
interested in a product automatically reveals that the buyer values it at
a high degree. Over 56% of all answers were 6 or above for this feature.
Nevertheless, there are peaks on each end of its histogram. On the second
level, the data displays that showing interest does not matter for carpet
dealers, and so it is for approximately half of the textile and gift sellers.
However, the jewellers and leather sellers seem to be sensitive to such
behaviour and would let the price get affected by showing interest. There
is also a big difference between owners and employees. Employees will
try to get more out of negotiations with an interested buyer. On the third
level, more or less the same results are observable with the one exception
that the employees of jewellery stores caused the outcome on the second
level, the owners gave moderate answers.
69. 9.2. RESULTS 55
Wearing Apparel
This buyer’s feature has very balanced4 results on the first level. 53% of all
responses were a 5 or below. On the second level, the results are balanced
as well, except for carpet sellers who seem not to care how the wearing
apparel of their customers are, on the contrary, leather sellers in general
care a lot. On the third level, we can add the employees of gift shops to
the group of leather sellers. It must be noted that the employees of gift
shops gave high answers in general. This can be explained with their age.
74% of the sellers are under 35 years old, whereas the share of merchants
under 35 is at 43% in the surveyed population.
Accent
A customer’s accent was through all levels and all clusters unimportant,
except for employees of gift shops. Their answers were balanced. The
same is observable in the second section of the questionnaire in which
over 80% of the interviewees did not agree with the statement that an
accent-free speaking of Turkish lowers the price.
Sympathy
This characteristic has the second highest mean and the highest median.
It seems not rational for sellers to let themselves influence by sympathy,
but 63% of all answers were 6 or higher. Only carpet dealers and the
textile sellers delivered balanced results in their answers. All other clusters
set their initial price lower if their customer is pleasant. This extreme
results are caused by the employees, who are much more affected by this
characteristic. The shop owners gave balanced answers.
Number of Articles
This is the characteristic which has the highest mean and median. Almost
72% of all the answers were 6 or above in the first section of the question-
4Balanced means in this context that peaks appear on both sides of the histogram.
70. 56 CHAPTER 9. THE FIELD RESEARCH
naire. The results are even higher in the second section in which over 81%
agreed or strongly agreed that a higher quantity reduces the price. This
result was expected, since in the western civilisations a quantity discount
is common practice as well. The results look the same on each level, only
the jewellery shop owners gave balanced answers to this question. The
quantity discount seems to lose a part of its effect when it comes to really
expensive goods.
Time of the Day
This is one feature on which all the different groups had the same opinion
in general. The time does not seem to matter a lot. Although almost
19% of all merchants said that prices decrease when closing time comes
closer, in order to increase the daily profits. Many had the opinion that
on the contrary they would charge a higher price for their goods because
their customers would not have enough time to walk around and look
for cheaper alternatives anymore. It would be also likely that a customer
trying to buy something at such a late hour must be desperate and would
therefore lose his bargaining power. The prior belief that late shopping
gives buyers an advantage proved to be a myth. Nevertheless, it must be
noted that a majority of the sellers believe in siftah. This Turkish word
means the first sell of the day. They plead that the first sell of the day is
the hardest and business starts running faster after it. This means that
they are ready to agree on a rather low price early in the morning, some
of them even on a price with a margin equal to zero. This only proves
that most of the sellers at the Bazaar are superstitious at some degree and
sometimes act irrational.
Date
The results from the first section show that off-season some sellers decrease
their prices, but in general the date does not have a big impact on the
price. Nevertheless, merchants who were interviewed for a longer period
of time, explained that in this particular year in which customers were
71. 9.2. RESULTS 57
rare, they even sell products for their production costs, in order to reduce
their stocks and gain some liquidity for their business. Moreover, it is
possible that there was a misunderstanding in the first section. In the
second question of the questionnaire, in which off-season was particularly
mentioned, over 45% of the sellers answered that they lower their prices
off-season.
Wanting a Receipt
Based on a well known problem in Turkey, buyers often get discounts if
they waive to get a receipt after a purchase. No receipt means no taxes
and the decrease in future losses can be split between buyer and seller.
However, the results display that this must have changed in Turkey over
the last decade, at least in the Grand Bazaar. This feature has the lowest
mean and median and over 82% of all merchants gave an answer of 5 or
below.
Paying in Cash
The results for this parameter look balanced on the first level, although
this changes one level deeper. For the gift and textile sector it is more
important that their customers pay in cash than in the others. This can
easily be explained by the transactional fees the credit card companies
charge the stores. This fees are charged for every transaction and typically
consist of a percentage of each transaction accompanied by a flat per
transaction fee. The first part in which a percentage of the purchase is
charged applies to all stores but the second part is for gift and textile
sellers higher in proportion to the prices they charge for their goods then
for a jeweller.
Other Characteristics
There were only 13 sellers who actually used the blank spaces to add char-
acteristics they thought were important. 5 of the 13 interviewees wrote that
72. 58 CHAPTER 9. THE FIELD RESEARCH
Table 3: Correlation Matrix
min max range discount
age 0.157 0.145 0.102 0.129
nationality 0.217 0.264 0.220 0.325
gender −0.005 0.044 0.056 0.106
interest 0.100 0.178 0.170 0.277
wearing 0.127 0.220 0.208 0.327
accent 0.150 0.230 0.211 0.330
sympathy 0.106 0.131 0.110 0.240
number 0.088 0.184 0.183 0.227
time 0.130 0.198 0.181 0.288
date 0.007 0.138 0.165 0.286
receipt −0.028 −0.049 −0.047 0.112
cash 0.011 −0.070 −0.091 0.231
min 1 0.618 0.283 0.338
max 0.618 1 0.929 0.465
range 0.283 0.929 1 0.409
discount 0.338 0.465 0.409 1
being a regular customer and/or coming to the shop by recommendation
affects the price a lot. This gives a hint that reputation effects are present
in the Grand Bazaar. The following three features can be summarised into
one category, the merchants said that the customer should be respectful,
serious and under no circumstances behave like a "smarty pants". These
three features will affect the price negatively if the seller is not pleased
with a buyer’s behaviour. They all relate to the characteristic "sympathy".
For 4 of the sellers a buyer’s profession is an important feature. For
instance, if a buyer is a merchant himself then the price will probably
be affected by this. Last but not least, experience was mentioned by the
sellers. A buyer who has a lot of experience and knowledge in one sector
will get lower prices.
74. 60 CHAPTER 9. THE FIELD RESEARCH
Range and Discount
Consider table 3 in which the different correlations of buyer’s characteris-
tics to price ranges5 and discount during negotiations are pictured. There
is no remarkable correlation between any characteristic and any cost re-
lated value (min, max, range, discount). From the price range distributions
in table 4 it can be identified that especially leather and gift sellers have
wide price ranges. Whereas this result is expected for gift sellers as a
reason of very low production costs for some of their items, it is harder to
justify the results for sellers of leather products, especially for the results
above 70%. Although, gift and leather sellers have similar distributions
in table 4, their distributions in table 5 differ a lot. Leather dealers are
much more unlikely to give high discounts on their products. One of the
leather sellers mentioned that he would not give a high discount even
if he set the initial price extremely high above his costs. He would stick
to his strategy and try to get a high profit out of the deal. A discount
which exceeds a certain amount does not always increase the probability
of an agreement. At one point a potential buyer gets suspicious and asks
himself how such a high discount is possible. He may even question a
product’s quality or even the seller’s honesty which can easily lead to an
abortion of negotiation.
The jewellers have the tightest price ranges which is also an expected
results, for the same reason as for gift sellers. Since their production costs
are much higher, their price ranges vary a lot less in relation to their costs.
It must be noted that at the 10% mark they get undercut by the textile
sellers. The reason for that is, that there are a rising number of textile
dealers who work with fixed prices. They write prices on their goods,
like fashion stores in Western countries do, which eliminates the price
range. This does not mean that they do not negotiate at all, but they give
lower discounts than other stores. The carpet sellers seem to have a great
flexibility in setting their prices regardless of their expensive products.
5The price range is the difference between what a seller would add max and min on
top of his costs.
75. 9.3. IMPLICATIONS 61
Prices for carpets can vary a lot, especially if they are handmade and for
a layman it is hard to determine their value. For this reason and for the
uniqueness of handmade carpets, the carpet dealers gain more flexibility
in their price settings and in their range for negotiations.
9.3 Implications
One of the purposes of this thesis was to find important characteristics
of a buyer to recommend an optimal strategy for those who want to go
shopping at the Grand Bazaar of Istanbul. The optimal customer can be
inferred from the results in the previous section. To make a seller believe
that one has a very low reservation value and to find an agreement on the
lowest possible price6, a buyer should fulfil following characteristics or
should send someone instead who does.
• The ideal customer should be a young, local student.
• He should desist from showing interest in the desired product.
• He should wear cheap clothes.
• He must find a way to bond with the seller so that he likes him.
In order to achieve that, he must act serious and respectful and he
must reveal his knowledge about the sector and its goods without
sounding like a "smarty pants".
• He should concentrate on buying goods off-season and visit the
Bazaar as early in the morning as possible to benefit from from the
seller’s superstition of "siftah".
• If it is possible, he should buy as many items as possible from one
and the same store and should return to the same store again every
time he needs similar items. This way he will gain a status as a
regular and profit from lower prices.
6Idealy at the sellers reservation value.
