2. Announcements
• Pass Homework 2 to the aisle!
• Lisa will check off your names, and you can pick
up at end of class.
• Expect Homework 3 to be posted by Wednesday.
• Midterm isn’t until May 3, but make sure to catch
up if ASAP if you find yourself falling behind
• Definitely come to my office hours if you’re
confused!
3. Last Class
• Finished our discussion of market power
• We spoke about how oligopolists, in particular,
might compete with one another to set the
lowest price. Segue…
• Today, we will formalize our understanding of
strategic interaction by introducing the
fundamentals of game theory.
4. Learning Goals for Today
• Be able to summarize the elements of a
``game.’’
• Recognize the dominant strategies of a game.
• Discern the Nash equilibria of a game.
5. How will we do this?
• We will both:
– define a games generally (abstractly).
– work through explicit examples including two
competing oligopolists.
6. Game Theory
• Game theory helps us analyze situations in which the benefit
of a given action depends on the actions of others.
• Three elements of any game
• (1) Players: The decision makers.
• (2) Strategies: The actions players can take.
• (3) Payoffs: The rewards for each possible combination of
actions.
7. Advertising Game
• Players: AT&T and Verizon
• Strategies: Raise advertising spending or not.
• Payoffs:
– Both leave spending unchanged: 1.5 million each
– Both increase spending (hurt each other): 1 million each
– AT&T increases spending, Verizon does not (AT&T hurts
Verizon): AT&T 2 million, Verizon 500k
– Verizon increases spending, AT&T does not (Verizon hurts
AT&T): Verizon 2 million, AT&T 500k.
8. Payoff Matrix for Advertising Game
AT&T
Increase Leave Spending
Spending Unchanged
Increase 1 million (Vz) 2 million (Vz)
Spending 1 million (ATT) 0.5 million (ATT)
Verizon
Leave
0.5 million (Vz) 1.5 million (Vz)
Spending
2 million (ATT) 1.5 million (ATT)
Unchanged
9. Dominant Strategies
• Dominant strategy: a strategy that yields a higher payoff not
matter what the other player does.
• Dominated strategy: any other strategy available to a player
who has a dominant strategy.
• In the advertising game did the players have a dominant
strategy?
• When players have dominant strategies, it’s easy to see what
the outcome of the game will be.
10. Equilibrium
• Nash equilibrium: a game is said to be in equilibrium if each
player’s strategy is the best he or she can choose, given the
other players choices.
• A set of mutual best responses.
– How are these defined?
11. Payoff Matrix for Advertising Game 2
AT&T
Increase Leave Spending
Spending Unchanged
Increase 1 million (V) 1.5 million (V)
Spending 1 million (A) 1.2 million (A)
Verizon
Leave
1.2 million (V) 0.5 million (V)
Spending
1.8 million (A) 2 million (A)
Unchanged
12. Payoff Matrix for Advertising Game 3
AT&T
Increase Leave Spending
Spending Unchanged
Increase 1 million (V) 1.1 million (V)
Spending 1.5 million (A) 1 million (A)
Verizon
Leave
1.8 million (V) 2 million (V)
Spending
1 million (A) .5 million (A)
Unchanged
13. The Prisoner’s Dilemma
Criminal 1
Confess Deny
-10 (S) -1 (S)
Confess
-10 (L) -25 (L)
Criminal 2
-25 (S) 0 (S)
Deny
-1 (L) 0 (L)
14. Other Examples of the Prisoner’s
Dilemma
• Shouting at parties.
• People crowding around the baggage claim area at airports.
• Curbing CO2 emissions to slow climate change.
• Global arms race.
• Lance Armstrong.
15. How do two agents get out of this
dilemma?
• The dilemma: both agents have dominant, but suboptimal
strategies.
• Ideally, both agents’ dominant strategy would be the optimal
contract.
• Consider writing a contract to enforce the best outcome.
16. Recall the Original Advertising Game
AT&T
Increase Leave Spending
Spending Unchanged
Increase 1 million (Vz) 2 million (Vz)
Spending 1 million (ATT) 0.5 million (ATT)
Verizon
Leave
0.5 million (Vz) 1.5 million (Vz)
Spending
2 million (ATT) 1.5 million (ATT)
Unchanged
Contract: If I cheat, I pay the other no less than X dollars.
17. What X makes (No Chg, No Chg) a
Nash Equilibrium?
A. 0 million
B. 0.5 million
C. 1 million
D. 1.5 million
E. 2 million
18. The Economics of Cartels
• Cartel: any group of firms that agree to restrict output for the
purpose of earning an economic profit.
• But cartels are notoriously hard to maintain. Why?
• Example:oligopolists Boeing and Airbus
P
$1 million
Profit MC=ATC
$600 million
MR D
1000 Q (in thousands)
19. Payoff Matrix for a Cartel Agreement
Boeing
P=$1 million P=$999,999
(Cooperate) (Defect)
P=$1 million $300 million (A) 0 (A)
(Cooperate) $300 million (B) ≈$600 million (B)
Airbus
P=$999,999 ≈$600 million (A) ˂$300million (A)
(Defect) 0 (B) ˂$300 million (B)
