Learning Objectives
Game Theory
Game Theory
• New set of tools
• Describe how a small number of “players”
(e.g., firms) interact with each other in
competitive settings
• Important elements
• Consideration of rivals’ actions and responses
• “Look forward, reason back”
• Foot race vs. chess
Game Theory and the World
• Applicable in a host of settings
Game Theory and the World
• Applicable in a host of settings
Game Theory and the World
• Applicable in a host of settings
Game Theory and the World
• Applicable in a host of settings
Learning Objectives
1. List the basic elements of a game
2. Identify and explain the prisoner’s dilemma
and how it applies to real-world situations
3. Discuss strategies that enable players to
reap gains through cooperation
4. Explain games in which the timing and
commitment of players’ choices matter
The Elements of a Game
An Example
• “In a taste of a price war resembling that of airlines’ fare
wars, Amazon.com’s two biggest competitors wasted no
time matching the top online retailer’s 50 percent
discount on New York Times bestsellers.”
• “…Within hours of Amazon’s volley Monday,
barnesandnoble.com and Borders.com followed suit…”
• “…shares of Amazon (Nasdaq: AMZN) fell 6 percent, or
$6.56, to close Monday at $125.81. New York-based
Barnes & Noble, Inc. (BKS), saw its shares fall $1.12, to
$33.19. Shares of Ann Arbor, Michigan-based Borders
Group declined 50 cents, to $15.875.”
Definitions
• Basic elements of a game
• The players (e.g., firms)
• Their available strategies (e.g., prices)
• The payoff to each player for each possible
combination of strategies (e.g., profits)
• Start with a simple illustration
Pricing Game
• Two firms (players), A and B
• Each can pick low price or high price (two
strategies)
• Payoffs to each player are profits
• Assumption: both players choose without
knowing the other player’s strategy
Pricing Game
High
High
B
Low
, 12
, 20
,2
,8
A
Low
, B payoff
Equilibrium in Games
Equilibrium
• For each strategy that an opponent might
choose, a player can determine the
strategy that is a best response
• An equilibrium (Nash equilibrium) is a set
of strategies that are best responses to
each other:
• That is, no one player wants to unilaterally
change strategy
Best Responses
• To identify a best response, pick a strategy
for one player, and see what strategy for
the other player maximizes its payoff
• Continue for all possible strategies for
each player
Pricing Game
High
High
B
Low
, 12
, 20
,2
,8
A
Low
, B payoff
Best Responses
B’s best response
A’s best response
A picks L
A picks H
L
L
B picks L
B picks H
L
L
Pricing Game
High
High
B
Low
, 12
, 20
,2
,8
A
Low
, B payoff
Equilibrium
• A dominant strategy is one that yields a
higher payoff no matter what the other
player does (it is the best response to all
opponents’ strategies)
• A dominated strategy is available to a
player who has a dominant strategy, but
ruled out by the dominant strategy
The Prisoner’s Dilemma
Prisoner’s Dilemma
• Here, the equilibrium of the game is (L, L):
low prices by each firm
• Yields payoffs of (8, 8)
• But this is much worse for both players than
(H, H) which yields (12, 12)
• Why can’t players reach the high-price
equilibrium?
• The “prisoner’s dilemma”
Prisoner’s Dilemma
B
Don’t
Confess
A
Confess
Don’t Confess
Confess
A: 2 years jail
B: 2 years jail
A: 10 years jail
B: Freedom
A: Freedom
B: 10 years jail
A: 6 years jail
B: 6 years jail
Prisoner’s Dilemma
B
Don’t
Confess
A
Confess
Don’t Confess
Confess
A: 2 years jail
B: 2 years jail
A: 10 years jail
B: Freedom
A: Freedom
B: 10 years jail
A: 6 years jail
B: 6 years jail
Solving Games
Advertising Game
Increase
Increase
B
Cut
, 12
, 10
, 20
, 16
A
Cut
, B payoff
Advertising Game
Increase
Increase
B
Cut
, 12
, 10
, 20
, 16
A
Cut
, B payoff
Takeaways
Some Takeaways
• Equilibrium may or may not be the set of
strategies that is “best” in terms of payoffs
• Equilibrium does not require dominant
strategies for both (or even one) player
• A game may have zero, one, or multiple
equilibria
Games With No Equilibrium?
Achieving Cooperation
The Prisoner’s Dilemma
• Examples abound in and out of economics:
•
•
•
•
•
Price wars (airlines, DRAM, satellite radio)
Advertising
Campaign spending
Arms races
Bidding for professional sports players, oil tracts, etc.
• Cooperation in such settings is far more
valuable than playing the prisoner’s dilemma
• How to resolve?
Avoiding the Prisoner’s
Dilemma
Solving the Dilemma
• Repeated play and interaction can solve
the dilemma
• Repeated play:
•
•
•
•
Frequency of interaction
Stability of players
Length of game
Quality of information
Timing and Commitment
Timing Matters in Games
• Prisoner’s dilemma assumes simultaneous
decisions
• Not always true, sometimes one player gets
to move first
• Example: Viper and Corvette hybrid
models
• See how timing affects outcome of the game
• Look at simultaneous choices first
Car Model Choice Game
Viper
Hybrid
Hybrid
No hybrid
C: $60 m.
V: $60 m.
C: $80 m.
V: $70 m.
C: $70 m.
V: $80 m.
C: $50 m.
V: $50 m.
Corvette
No hybrid
Car Model Choice Game
Viper
Hybrid
Hybrid
No hybrid
C: $60 m.
V: $60 m.
C: $80 m.
V: $70 m.
C: $70 m.
V: $80 m.
C: $50 m.
V: $50 m.
Corvette
No hybrid
Sequential Play
Sequential Play
Commitment and Moving First
Sequential Play and Commitment
• Key in the sequential play example is commitment
or irreversibility
• Moving first allows commitment to a strategy
• Changes opponent’s options
• Value of commitment can be quite high:
•
•
•
•
•
•
Cortes’ ships
Excess capacity
Judo economics
Price-matching
Most-favored-customer clauses
Poison pills
Sequential Play and Moving First
• Moving first is best in the Viper/Corvette
game
• Also, in many other “winner-takes-all” markets
• Moving second can be better, too
• McDonald’s vs. Burger King
• Political positioning
Wrapping Up
Game Theory Takeaways
• Interdependence of decisions
• Think about best responses
• Look forward, reason back
• Rules of game matter
• Repeated play
• Sequential play
• Commitment
Learning Objectives
1. List the basic elements of a game
2. Identify and explain the prisoner’s
dilemma and how it applies to real-world
situations
3. Discuss strategies that enable players to
reap gains through cooperation
4. Explain games in which the timing and
commitment of players’ choices matter