Students should be able to: Use simple game theory to illustrate the interdependence that exists in oligopolistic markets Understanding the prisoners’ dilemma and a simple two firm/two outcome model. Students should analyse the advantages/disadvantages of being a first mover Students will not be expected to have an understanding of the Nash Equilibrium

1. Oligopoly and Game Theory
Topic 3.3.9

2. Oligopoly and Game Theory
Topic 3.3.9
Students should be able to:
• Use simple game theory to illustrate the interdependence that
exists in oligopolistic markets
• Understanding the Prisoners’ Dilemma and a simple two
firm/two outcome model.
• Students should analyse the advantages/disadvantages of being a
first mover
• Students will not be expected to have an understanding of the
Nash Equilibrium

3. Game Theory and Oligopoly
Game theory is the study of
how people and businesses
behave in strategic situations
(i.e. when they must consider
the effect of other people’s
responses to their own actions).
A game consists of:
1. Players
2. Strategies
3. Payoffs
4. It might also involve some
form of pre-commitment
Oligopoly theory often
makes heavy use of game
theory to model the actual
behaviour of businesses in
concentrated markets

4. Different Types of Games
• Simultaneous Games
– When players effectively make decisions at the same time
– They don’t know the choices of other players when
making their choices
– Examples:
• The Prisoners’ Dilemma
• A game of Rock, Paper, Scissors
• Split or Steal in Golden Balls
• Individual plays in a game of American Football
• Penalty shoot-outs in soccer matches
• Serving and receiving in Tennis
• Speed dating
• Closed bid auctions
• Athletes choosing to dope or not to dope

5. Different Types of Games
• Sequential games
– A sequential game is one in which the players take
alternate turns to make their choices.
– Examples:
• A game of chess
• Open-outcry auctions with sequential bidding
• Salary negotiations between employer and employee
• Haggling with a trader to buy a second hand car
• Making offers on a property
– It is important to know who is going to move first in a
sequential game as their may be a first mover
advantage, or even a first mover disadvantage

6. Repeated versus One-Shot Games
• One-Shot Games
– This is a game that is played only once
– The pay-off may be such that a game might be
impossible to play twice
– E.g. mutually assured nuclear destruction
– Slightly different with tactical / conventional warfare
– In one-shot interaction, people often have an
incentive to behave opportunistically / selfishly
– Consider a one shot Prisoners’ Dilemma game where
an individual wants to minimise their own sentence

7. Repeated versus One-Shot Games
• Repeated games – a game played more than once
– A feature of applied business – e.g. decisions on:
• Pricing (Established supermarkets versus the Deep Discounters)
• The size of marketing budgets (Coca Cola v Pepsi)
• Research and development spend (Samsung v Apple v Huawei)
• Capital investment and supply capacity forecasts (Cruise ships)
– There is more scope for co-operative strategies to emerge
– Credible threat power – history of past behaviours
– Agents “learn by doing” – if someone continually serves
to your backhand in tennis, your backhand will improve
– Repeated games – crucial point is the reaction to a
defective strategy by another player
• Tit for Tat Strategy – if you defect, I defect in the next round
• Grim Strategy – if you defect, I will defect in all future rounds

8. Valuing the future in repeated games
• If you get punished tomorrow for bad behaviour
today and you value the future sufficiently highly,
it is probably in your own self-interest to behave
well today!
• Application:
– Fines applied to price fixing and other anti-
competitive cartels
– After a cartel fine … how likely is the cartel to reform?
– Are students who have taken an Economics degree
less likely to behave cooperatively in their adult lives?

9. Game Theory – Prisoners’ Dilemma
Prisoner B
Silent Betray
Prisoner A
Silent (6M,6M) (10Y,0)
Betray (0,10Y) (5Y,5Y)
Comment on the best strategies for each player and the
likely outcome in this game

10. Game Theory – Prisoners’ Dilemma
Prisoner B
Silent Betray
Prisoner A
Silent (6M,6M) (10Y,0)
Betray (0,10Y) (5Y,5Y)
Comment on the best strategies for each player and the
likely outcome in this game
• The prisoners' dilemma is
a particular game that
illustrated why it is
difficult to cooperate,
even when it is in the best
interest of both parties.
• Both players are assumed
to select their own
dominant strategies for
short-sighted personal
gain / self-interest.
• Eventually, they reach an
equilibrium in which they
are both worse off than
they would have been, if
they could both agree to
select an alternative (non-
dominant) strategy.

11. Prisoners’ Dilemma – Decision Trees
Prisoner B
Silent Betray
Prisoner
A
Silent (6M,6M) (10Y,0)
Betray (0,10Y) (5Y,5Y)

12. Nash Equilibrium
• Nash Equilibrium is an important idea in game
theory
• It describes any situation where all of the
participants in a game are pursuing their best
possible strategy given the strategies of all of the
other participants.
• In a Nash Equilibrium, the outcome of a game
that occurs is when player A takes the best
possible action given the action of player B, and
player B takes the best possible action given the
action of player A

13. Game Theory: A Simple Pricing Game
Firm B (right hand figures below)
Expected
Profit ($bn)
High Prices Low Prices
Firm
A
High Prices $3bn; $3bn $0bn, $5bn
Low Prices $5bn; $0bn $1bn, $1bn
In this two firm game, they have to decide whether to set high or low prices
The table shows the profits (pay-offs) that results from each set of choices
The grid above shows a pay-off matrix – it shows a simple pricing game between firm A
and firm B. They are assumed to choose their prices at the same time

14. A Simple Pricing Game
Firm B (right hand figures below)
Expected
Profit ($bn)
High Prices Low Prices
Firm
A
High Prices $3bn; $3bn $0bn, $5bn
Low Prices $5bn; $0bn $1bn, $1bn
To understand the game we isolate one firm and assume that Firm B makes the
first decision. Assume that each firm is a profit maximiser.
The grid above shows a pay-off matrix – it shows a simple pricing game between firm A
and firm B. They are assumed to choose their prices at the same time

15. A Simple Pricing Game
B
Profit $bn High Prices Low Prices
A
High Prices $3bn; $3bn $0 bn, $5bn
Low Prices $5bn; $0bn $1bn, $1bn
In this game, regardless of what the other firm decides to do, the best response
of the other firm is to charge a lower price – they may settle at this low price
The grid above shows a pay-off matrix – it shows a simple pricing game between firm A
and firm B. They are assumed to choose their prices at the same time

16. Pricing Game – Incentives to Collude
B
Profit $bn High Prices Low Prices
A
High Prices $3bn; $3bn $0 bn, $5bn
Low Prices $5bn; $0bn $1bn, $1bn
If these firms got together and decided to collude by both setting a high price,
then both of them would earn higher total profits – this would be pareto optimal
The grid above shows a pay-off matrix – it shows a simple pricing game between firm A
and firm B. They are assumed to choose their prices at the same time

17. First Mover Advantage
Two players A and B take turns
choosing a number between 1
and 10 (inclusive)
A goes first
The cumulative number of ALL
of the numbers chosen is
calculated as the game
progresses
The winner is the player whose
choice of number TAKES THE
TOTAL to 100 or more
Does this game have first
mover advantage?

18. First Mover Advantage – 0 to 100 Game
• For Player A to win, he/she must a number
that takes the total to 100 or more
• The only way this can happen is Player B to
leave me a number of 90 or more
• Player A needs to ensure Player B is left
with 89
• Player B knows this too
• Player A needs to leave Player B with 78
• Use backward-induction to work towards
the solution
• 100 – 89 – 78 – 67 – 56 – 45 – 34 – 23 – 12
• Player A can ensure he/she wins by going
first and choosing 1

19. Examples of First Mover Advantage
Just Eat Golden Leaf
Holdings
Oculus Rift Spotify
Amazon Web
Services
Infrastructure
Investment Banks
AWS has become the biggest technology
infrastructure provider in the world — and
it is also the fastest growing and most
profitable part of Amazon

20. Evaluating First Mover Advantage
Advantages of being the first mover
• A business first into the market can develop a significant
competitive advantage through learning by doing - making it
difficult and costly for new firms/rivals to enter
• They can exploit internal economies of scale (leading to lower
LRAC) and also build brand loyalty/ repeat demand
• Consumer behaviour can become habitual – hard to eat into!
Critical evaluation points
• Employees from first mover may leave to set up challenge brands –
taking some of the intellectual capital with them
• First movers are often unprofitable, the failure rate can be high
• Second-movers can learn much from first mover mistakes
• First scaler advantage may be more important than first mover

21. Game Theory: The Stag Hunt
• Two hunters
• Within range is one stag
and two hares
• Both hunters must chase
the stag to catch it and
share the meat
• The two hares can be
caught individually
• The meat from one stag >
the meat from two hares

22. The Stag Hunt
Pay-offs from hunting in
terms of units of meat
Player 2
Stag Hare
Player 1
Stag (3 , 3) (0, 2)
Hare (2, 0) (1, 1)

23. The Ultimatum Game
• In the basic ultimatum game:
1. The first player (the proposer) receives a sum of
money and proposes how to divide the sum between
the proposer and the other player
2. The second player (the responder) chooses to either
accept or reject this proposal
3. If the second player accepts, the money is split
according to the proposal
4. If the second player rejects, neither player receives
any money
5. The ultimatum game is often played once – what is
the equilibrium choice for Player 1?

24. The Ultimatum Game - Tweaked
• The first player (the proposer) receives a sum of
money and proposes how to divide the sum between
the proposer and the other player
• The second player (the responder) chooses to either
accept or reject this proposal
• If the second player accepts, the money is split
according to the proposal
• The second player can
• Reject the offer and end the game
• Propose a counter-offer

25. Discussing the Ultimatum Game
• People value things other than money!
• They care about fairness (equity)
• The size of the bargaining pie will shape people’s
willingness to accept a seemingly inequitable offer
• Repeated games / options to make counter-offers
may change the behaviour of players
• Are players maximisers or satisficers?
• Professionally trained economists nearly always
offer less than “normal” people!

26. Rock Paper Scissors – Nash Equilibrium?
In the famous Rock, Paper, Scissors game: Rock > Scissors, Paper > Rock and
Scissors > Paper. Is there an optimum strategy when playing this game?
Rock Paper Scissors
Rock ( 0, 0) (-1 , 1) (1, -1)
Paper (1, -1) (0, 0) (-1, 1)
Scissors (-1, 1) (1, -1) (0, 0)

27. Rock Paper Scissors – Random Strategy
Rock Paper Scissors
Rock ( 0, 0) (-1 , 1) (1, -1)
Paper (1, -1) (0, 0) (-1, 1)
Scissors (-1, 1) (1, -1) (0, 0)
In this game matter what both players choose, at
least one of them can always improve their payoff by
switching to a different choice. If one of them wins
the game, the loser can improve their payoff by
switching. If it's a tie, either player can improve their
payoff by switching to a different choice.

28. Key Concepts – Game Theory
Cooperative outcome
An equilibrium in a game where the players
agree to cooperate
Dominant strategy
A dominant strategy is one where a single
strategy is best for a player regardless of what
strategy other players in the game decide to use
Nash equilibrium
Any situation where all participants in a game are
pursuing their best possible strategy given the
strategies of all of the other participants
Tacit collusion
Where firms undertake actions that are likely to
minimize a competitive response, e.g. avoiding
price-cutting or not attacking each other’s market
Whistle blowing
When one or more agents in a collusive
agreement report it to the authorities
Zero sum game
An economic transaction in which whatever is
gained by one party must be lost by the other.

29. Applications of Game Theory
• Interdependent pricing in an oligopoly
– Price wars in concentrated markets
• Decisions on
– Research and development
– Marketing budgets
– New product launches
– Output decisions
• Co-operative behaviour and collaboration
between businesses (requires trust and
recognition of mutually beneficial outcomes)

30. Oligopoly and Game Theory
Topic 3.3.9