1. Game Theory: Inside Oligopoly
Chapter 10
Game Theory:
Inside Oligopoly
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Chapter Outline Overview of games and strategic thinking
Chapter Overview
Chapter Outline
Overview of games and strategic thinking
Simultaneous-move, one-shot games
Theory
Application of one-shot games
Infinitely repeated games
Factors affecting collusion in pricing games
Application of infinitely repeated games
Finitely repeated games
Games with an uncertain final period
Games with a known final period: the end-of-period problem
Multistage games
Applications of multistage games

3. Chapter Overview
Introduction
Chapter 9 examined market environments when only a few firms compete in a market, and determined that the actions of one firm will impact its rivals. As a consequence, a manager must consider the impact of her behavior on her rivals.
This chapter focuses on additional manager decisions that arise in the presence of interdependence. The general tool developed to analyze strategic thinking is called game theory.

4. Overview of Games and Strategic Thinking
Game Theory Framework
Game theory is a general framework to aid decision making when agents’ payoffs depends on the actions taken by other players.
Games consist of the following components:
Players or agents who make decisions.
Planned actions of players, called strategies.
Payoff of players under different strategy scenarios.
A description of the order of play.
A description of the frequency of play or interaction.

5. Order of Decisions in Games
Overview of Games and Strategic Thinking
Order of Decisions in Games
Simultaneous-move game
Game in which each player makes decisions without the knowledge of the other players’ decisions.
Sequential-move game
Game in which one player makes a move after observing the other player’s move.

6. Frequency of Interaction in Games
Overview of Games and Strategic Thinking
Frequency of Interaction in Games
One-shot game
Game in which players interact to make decisions only once.
Repeated game
Game in which players interact to make decisions more than once.

7. Theory Strategy Normal-form game
Simultaneous-Move, One-Shot Games
Theory
Strategy
Decision rule that describes the actions a player will take at each decision point.
Normal-form game
A representation of a game indicating the players, their possible strategies, and the payoffs resulting from alternative strategies.

8. Normal-Form Game Simultaneous-Move, One-Shot Games Set of players
Player B’s strategies
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player B’s
possible
payoffs
from
strategy
“right”
Player A’s strategies
Player A’s possible payoffs
from strategy “down”

9. Possible Strategies Dominant strategy Secure strategy
Simultaneous-Move, One-Shot Games
Possible Strategies
Dominant strategy
A strategy that results in the highest payoff to a player regardless of the opponent’s action.
Secure strategy
A strategy that guarantees the highest payoff given the worst possible scenario.
Nash equilibrium strategy
A condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy, given the other players’ strategies.

10. Dominant Strategy Player A has a dominant strategy: Up
Simultaneous-Move, One-Shot Games
Dominant Strategy
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A has a dominant strategy: Up
Player B has no dominant strategy

11. Simultaneous-Move, One-Shot Games
Secure Strategy
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A’s secure strategy: Up … guarantees at least a $10 payoff
Player B’s secure strategy: Right … guarantees at least an $8 payoff

12. Nash Equilibrium Strategy
Simultaneous-Move, One-Shot Games
Nash Equilibrium Strategy
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
Player A
Player B
Strategy
Left
Right Up
10, 20
15, 8
Down
-10 , 7
10, 10
A Nash equilibrium results when Player A’s plays “Up”
and Player B plays “Left”

13. Application of One-Shot Games: Pricing Decisions
Simultaneous-Move, One-Shot Games
Application of One-Shot Games: Pricing Decisions
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -10
-10 , 50
10, 10
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -10
-10 , 50
10, 10
A Nash equilibrium results when both players charge “Low price”
Payoffs associated with the Nash equilibrium is inferior from the
firms’ viewpoint compared to both “agreeing” to charge
“High price”: hence, a dilemma.

14. Application of One-Shot Games: Coordination Decisions
Simultaneous-Move, One-Shot Games
Application of One-Shot Games: Coordination Decisions
Firm A
Firm B
Strategy
120-Volt Outlets
90-Volt Outlets
$100, $100
$0, $0
$0 , $0
Firm A
Firm B
Strategy
120-Volt Outlets
90-Volt Outlets
$100, $100
$0, $0
$0 , $0
Firm A
Firm B
Strategy
120-Volt Outlets
90-Volt Outlets
$100, $100
$0, $0
$0 , $0
There are two Nash equilibrium outcomes associated with this game:
Equilibrium strategy 1: Both players choose 120-volt outlets
Equilibrium strategy 2: Both players choose 90-volt outlets
Ways to coordinate on one equilibrium:
1) permit player communication
2) government set standard

15. Application of One-Shot Games: Monitoring Employees
Simultaneous-Move, One-Shot Games
Application of One-Shot Games: Monitoring Employees
Manager
Worker
Strategy
Monitor
Don’t Monitor
-1, 1
1, -1
There are no Nash equilibrium outcomes associated with this game.
Q: How should the agents play this type of game?
A: Play a mixed (randomized) strategy, whereby a player randomizes
over two or more available actions in order to keep rivals from
being able to predict his or her actions.

16. Application of One-Shot Games: Nash Bargaining
Simultaneous-Move, One-Shot Games
Application of One-Shot Games: Nash Bargaining
Management
Union
Strategy 50
100
0, 0
0, 50
0, 100
50 , 0
50, 50
-1, -1
100, 0
There three Nash equilibrium outcomes associated with this game:
Equilibrium strategy 1: Management chooses 100, union chooses 0
Equilibrium strategy 2: Both players choose 50
Equilibrium strategy 3: Management chooses 0, Union chooses 100

17. Infinitely Repeated Games
Theory
An infinitely repeated game is a game that is played over and over again forever, and in which players receive payoffs during each play of the game.
Disconnect between current decisions and future payoffs suggest that payoffs must be appropriately discounted.

18. Present Value Analysis Review
Infinitely Repeated Games
Present Value Analysis Review
When a firm earns the same profit, 𝜋, in each period over an infinite time horizon, the present value of the firm is:
𝑃𝑉 𝐹𝑖𝑟𝑚 = 1+𝑖 𝑖 𝜋

19. Supporting Collusion with Trigger Strategies
Infinitely Repeated Games
Supporting Collusion with Trigger Strategies
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
The Nash equilibrium to the one-shot, simultaneous-move
pricing game is: Low, Low
When this game is repeatedly played, it is possible for firms to
collude without fear of being cheated on using trigger strategies.
Trigger strategy: strategy that is contingent on the past play of a
game and in which some particular past action “triggers” a different
action by a player.

20. Supporting Collusion with Trigger Strategies
Infinitely Repeated Games
Supporting Collusion with Trigger Strategies
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
Trigger strategy example: Both firms charge the high price, provided
neither of us has ever “cheated” in the past (charge low price).
If one firm cheats by charging the low price, the other player will
punish the deviator by charging the low price forever after.
When both firms adopt such a trigger strategy, there are conditions
under which neither firm has an incentive to cheat on the collusive
outcome.

21. Trigger Strategy Conditions to Support Collusion
Infinitely Repeated Games
Trigger Strategy Conditions to Support Collusion
Suppose a one-shot game is infinitely repeated and the interest rate is 𝑖. Further, suppose the “cooperative” one-shot payoff to a player is 𝜋 𝐶𝑜𝑜𝑝 , the maximum one-shot payoff if the player cheats on the collusive outcome is 𝜋 𝐶ℎ𝑒𝑎𝑡 , the one-shot Nash equilibrium payoff is 𝜋 𝑁 , and 𝜋 𝐶ℎ𝑒𝑎𝑡 − 𝜋 𝐶𝑜𝑜𝑝 𝜋 𝐶𝑜𝑜𝑝 − 𝜋 𝑁 ≤ 1 𝑖 .
Then the cooperative (collusive) outcome can be sustained in the infinitely repeated game with the following trigger strategy: “Cooperate provided that no player has ever cheated in the past. If any player cheats, “punish” the player by choosing the one-shot Nash equilibrium strategy forever after.

22. Supporting Collusion with Trigger Strategies
Infinitely Repeated Games
Supporting Collusion with Trigger Strategies
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
Suppose firm A and B repeatedly play the game above, and the
interest rate is 40 percent. Firms agree to charge a high price in
each period, provided neither has cheated in the past.
Q: What are firm A’s profits if it cheats on the collusive agreement?
A: If firm B lives up to the collusive agreement but firm A cheats,
firm A will earn $50 today and zero forever after.

23. Supporting Collusion with Trigger Strategies
Infinitely Repeated Games
Supporting Collusion with Trigger Strategies
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
Q: What are firm A’s profits if it does not cheat on the collusive
agreement?
A: …= =$35

24. Supporting Collusion with Trigger Strategies
Infinitely Repeated Games
Supporting Collusion with Trigger Strategies
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
Q: Does an equilibrium result where the firms charge the high price
in each period?
A: Since $50>$35, the present value of firm A’s profits are higher
if A cheats on the collusive agreement. In equilibrium both firms
will charge low price and earn zero profit each period.

25. Factors Affecting Collusion in Pricing Games
Infinitely Repeated Games
Factors Affecting Collusion in Pricing Games
Sustaining collusion via trigger strategies is easier when firms know:
who their rivals are, so they know whom to punish, if needed.
who their rival’s customers are, so they can “steal” those customers with lower prices.
when their rivals deviate, so they know when to begin punishment.
be able to successfully punish rival.

26. Factors Affecting Collusion in Pricing Games
Infinitely Repeated Games
Factors Affecting Collusion in Pricing Games
Number of firms in the market
Firm size
History of the market
Punishment mechanisms

27. Finitely Repeated Games
Theory
Finitely repeated games are games in which a one-shot game is repeated a finite number of times.
Variations of finitely repeated games: games in which players
do not know when the game will end;
know when the game will end.

28. Games with Uncertain Final Period
Finitely Repeated Games
Games with Uncertain Final Period
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
Suppose the probability that the game will end after a given play is
𝜃, where 0<𝜃<1.
An uncertain final period mirrors the analysis of infinitely repeated
games. Use the same trigger strategy.
No incentive to cheat on the collusive outcome associated with a
finitely repeated game with an unknown end point above, provided:
Π 𝐴 𝐶ℎ𝑒𝑎𝑡 =50≤ 10 𝜃 = Π 𝐴 𝐶𝑜𝑜𝑝

29. Repeated Games with a Known Final Period: End-of-Period Problem
Finitely Repeated Games
Repeated Games with a Known Final Period: End-of-Period Problem
Firm A
Firm B
Strategy
Low price
High price
0, 0
50, -40
-40 , 50
10, 10
When this game is repeated some known, finite number of times
and there is only one Nash equilibrium, then collusion cannot work.
The only equilibrium is the single-shot, simultaneous-move Nash
equilibrium; in the game above, both firms charge low price.

30. Multistage Games
Theory
Multistage games differ from the previously examined games by examining the timing of decisions in games.
Players make sequential, rather than simultaneous, decisions.
Represented by an extensive-form game.
Extensive form game
A representation of a game that summarizes the players, the information available to them at each stage, the strategies available to them, the sequence of moves, and the payoffs resulting from alternative strategies.

31. Theory: Sequential-Move Game in Extension Form
Multistage Games
Theory: Sequential-Move Game in Extension Form
Player A payoff
Player B payoff
(10,15)
Decision node
denoting the
beginning of the
game Up B Up
Down
(5,5) A
(0,0)
Down Up
Player A feasible strategies: B Up
Down
Down
Player B’s decision nodes
Player B feasible strategies:
(6,20)
Up, if player A plays Down and Down, if player A plays Down
Up, if player A plays Up and Down, if player A plays Up

32. Equilibrium Characterization
Multistage Games
Equilibrium Characterization
(10,15) Up B Up
Down
(5,5) A
(0,0)
Down Up
Nash Equilibrium
Player A: Down
Player B: Down, if player A chooses Up,
and Down if Player A chooses Down B
Down
(6,20)
Is this Nash equilibrium reasonable?
No! Player B’s strategy involves a non-credible threat since if A plays Up,
B’s best response is Up too!

33. Subgame Perfect Equilibrium
Multistage Games
Subgame Perfect Equilibrium
A condition describing a set of strategies that constitutes a Nash equilibrium and allows no player to improve his own payoff at any stage of the game by changing strategies.

34. Equilibrium Characterization
Multistage Games
Equilibrium Characterization
(10,15) Up B Up
Down
(5,5) A
(0,0)
Down Up B
Subgame Perfect Equilibrium
Player A: Up
Player B: Up, if player A chooses Up,
and Down if Player A chooses Down
Down
(6,20)

35. Application of Multistage Games: The Entry Game
Nash Equilibrium I:
Player A: Out
Player B: Hard, if player A chooses In
(−1,1)
Hard
Non-credible, threat since if A plays
In, B’s best response is Soft B In
Soft
(5,5) A
Nash Equilibrium II:
Player A: In
Player B: Soft, if player A chooses In
Out
Credible. This is subgame perfect equilibrium.
(0,10)

36. Conclusion
Firms operating in a perfectly competitive market take the market price as given.
Produce output where P = MC.
Firms may earn profits or losses in the short run.
… but, in the long run, entry or exit forces profits to zero.
A monopoly firm, in contrast, can earn persistent profits provided that source of monopoly power is not eliminated.
A monopolistically competitive firm can earn profits in the short run, but entry by competing brands will erode these profits over time.