1. Game Theory and Strategic Play
Microeconomics
Second Edition
Chapter 13
Game Theory and Strategic Play
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2. Learning Objective
13.1 Simultaneous Move Games 13.2 Nash Equilibrium 13.3 Applications of Nash Equilibria 13.4 How Do People Actually Play Such Games? 13.5 Extensive-Form Games

3. Key Ideas (1 of 2) There are important situations when the
behavior of others affects your payoffs.
Game theory is the economic framework
that describes our optimal actions in such
settings.

4. Key Ideas (2 of 2)
A Nash equilibrium is a situation where none of the players can do better by choosing a different action or strategy.
Nash equilibria are applicable to a wide variety of problems, including zero-sum games, the tragedy of the commons, and the prisoners’ dilemma.

5. Game Theory and Strategic Play (1 of 3)
Evidence-Based Economics Example:
Is there value in putting yourself into someone else’s shoes in extensive form games?

6. Game Theory and Strategic Play (2 of 3)
In 1970, Congress was considering banning cigarette advertising on TV. When they held hearings on the issue, not a single representative from the cigarette industry showed up to argue against the legislation. Why?

7. Game Theory and Strategic Play (3 of 3)
Game Theory The study of strategic interactions

8. Simultaneous Move Games (1 of 6)
Elements of a game
The players
The strategies
The payoffs

9. Simultaneous Move Games (2 of 6)
The Prisoners’ Dilemma Game What happened: You and your partner in crime, Josie, got busted for robbery, caught in the act. The police separate you at the police station for questioning and offer each of you a deal…

10. Simultaneous Move Games (3 of 6)
If you both confess to having a gun, you each get 5 years. If you confess to having a gun during the crime, but Josie does not (you rat her out), you walk free and Josie gets 10 years. Josie gets the same deal—if she rats you out, she goes free and you get 10 years. If neither one of you confesses to the gun charge, you will each get 2 years for the robbery.

11. Simultaneous Move Games (4 of 6)
Elements of this game: 1. The players—you and Josie 2. The strategies—confess or not confess 3. The payoffs—given by a payoff matrix Payoff matrix Represents payoffs for each player for each strategy

12. Simultaneous Move Games (5 of 6)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
Simultaneous move game Players pick their strategies at the same time

13. Simultaneous Move Games (6 of 6)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma (2 of 6)
What should you do?

14. Simultaneous Move Games Best Responses and the Prisoners’ Dilemma (1 of 2)
Exhibit 13.2 Prisoners’ Dilemma Game with Your Partner Confessing
What if you think she will confess?

15. Simultaneous Move Games Best Responses and the Prisoners’ Dilemma (2 of 2)
Exhibit 13.3 Prisoners’ Dilemma Game with Your Partner Holding Out
What if you think she will NOT confess?

16. Simultaneous Move Games Dominant Strategies and Dominant Strategy Equilibrium (1 of 5)
Dominant strategy One player’s best response, regardless of what the other person does Dominant strategy equilibrium When each strategy used is a dominant strategy

17. Exhibit 13.1 Payoffs in the Prisoners’ Dilemma (3 of 6)
Simultaneous Move Games Dominant Strategies and Dominant Strategy Equilibrium (2 of 5)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma (3 of 6)

18. Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
Simultaneous Move Games Dominant Strategies and Dominant Strategy Equilibrium (3 of 5)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
But… you and Josie made a pact that if ever caught you would NOT rat each other out
Do you think that agreement will hold?

19. Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
Simultaneous Move Games Dominant Strategies and Dominant Strategy Equilibrium (4 of 5)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
No way! The incentive to cheat and confess “rat” on Josie is too high to ignore
IF you confess You get released From Josie’s point of view it’s the same payoff

20. Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
Simultaneous Move Games Dominant Strategies and Dominant Strategy Equilibrium (5 of 5)
Exhibit 13.1 Payoffs in the Prisoners’ Dilemma
Dominant Strategy For both you and Josie

21. Simultaneous Move Games without Dominant Strategies (1 of 9)
Do all games have dominant strategies? Surf shops and advertising

22. Simultaneous Move Games without Dominant Strategies (2 of 9)
Elements of this game:
The players—Hang Ten and La Jolla Surf
The strategies—advertise or don’t
The payoffs—given by a payoff matrix

23. Simultaneous Move Games without Dominant Strategies (3 of 9)
Exhibit 13.4 The Advertising Game

24. Simultaneous Move Games without Dominant Strategies (4 of 9)
Exhibit 13.4 The Advertising Game
Advertising is expensive Profits larger without that cost
BUT if we don’t advertise and our competitors do They get more business

25. Simultaneous Move Games without Dominant Strategies (5 of 9)
Exhibit 13.5 When La Jolla Surf Shop Advertises
What should you do if you think La Jolla will advertise?

26. Simultaneous Move Games without Dominant Strategies (6 of 9)
Exhibit 13.5 When La Jolla Surf Shop Advertises
What should you do if you think La Jolla will advertise?
If we think they will advertise Then we should advertise

27. Simultaneous Move Games without Dominant Strategies (7 of 9)
Exhibit 13.6 When La Jolla Surf Shop Does Not Advertise
What should you do if you think La Jolla will NOT advertise?
If we think they will not advertise Then we should also not advertise

28. Simultaneous Move Games without Dominant Strategies (8 of 9)
Exhibit 13.6 When La Jolla Surf Shop Does Not Advertise
What should you do if you think La Jolla will NOT advertise?

29. Simultaneous Move Games without Dominant Strategies (9 of 9)
What should you do? Advertise or not advertise?

30. Nash equilibrium (1 of 2)
Nash equilibrium Each player chooses a strategy that is best, given the strategies of others; i.e., changing strategies does not make anyone better off

31. Nash equilibrium (2 of 2) Two requirements for Nash equilibrium:
All players understand the game and the payoffs of each strategy
All players recognize that the other players understand the game and payoffs

32. Nash Equilibrium Finding a Nash Equilibrium (1 of 8)
Exhibit 13.4 The Advertising Game
If La Jolla advertises, you should advertise, too. Will you change your behavior?

33. Nash Equilibrium Finding a Nash Equilibrium (2 of 8)
Exhibit 13.4 The Advertising Game
If La Jolla advertises, you should advertise, too. Will you change your behavior?

34. Nash Equilibrium Finding a Nash Equilibrium (3 of 8)
Exhibit 13.4 The Advertising Game
If La Jolla does not advertise, you should not advertise, either. Will you change your behavior?

35. Nash Equilibrium Finding a Nash Equilibrium (4 of 8)
Exhibit 13.4 The Advertising Game
If La Jolla does not advertise, you should not advertise, either. Will you change your behavior?

36. Nash Equilibrium Finding a Nash Equilibrium (5 of 8)
There are two Nash equilibria for this game:
Both advertise
Both don’t advertise
What if the current position is not in one of these cells?

37. Exhibit 13.7 Two Nash Equilibria in the Advertising Game (1 of 4)
What if you are advertising but La Jolla is not?

38. Nash Equilibrium Finding a Nash Equilibrium (6 of 8)
Exhibit 13.7 Two Nash Equilibria in the Advertising Game
What if you are advertising but La Jolla is not?

39. Nash Equilibrium Finding a Nash Equilibrium (7 of 8)
Exhibit 13.7 Two Nash Equilibria in the Advertising Game
What if you are not advertising but La Jolla is?

40. Nash Equilibrium Finding a Nash Equilibrium (8 of 8)
Exhibit 13.7 Two Nash Equilibria in the Advertising Game
What if you are not advertising but La Jolla is?

41. Applications of Nash Equilibria Tragedy of the Commons Revisited (1 of 4)
Two interesting applications of Nash equilibria:
Tragedy of the commons
Soccer

42. Applications of Nash Equilibria Tragedy of the Commons Revisited (2 of 4)
Tragedy of the commons example:
Elements of this game
The players: Polluter 1 and Polluter 2
The strategies: Pollute or not
The payoff: Payoff matrix

43. Exhibit 13.8 Payoff Matrix for Two Polluting Plants
Applications of Nash Equilibria Tragedy of the Commons Revisited (3 of 4)
Exhibit 13.8 Payoff Matrix for Two Polluting Plants

44. They both end up here no matter where they start
Applications of Nash Equilibria Tragedy of the Commons Revisited (4 of 4)
Exhibit 13.8 Payoff Matrix for Two Polluting Plants
They both end up here no matter where they start
Firm 1 wants to move here
But this is best outcome for ALL but they cannot get their on their own. What can we do?
Firm 2 wants to move here

45. Game Theory and Strategic Play (1 of 4)
In 1970, Congress was considering banning cigarette advertising on TV. When they held hearings on the issue, no one from the cigarette industry showed up to argue against the legislation. Why?

46. Applications of Nash Equilibria The Zero-Sum Game (1 of 5)
Game theory is not just for business decisions— How you can be a better soccer player!

47. Applications of Nash Equilibria The Zero-Sum Game (2 of 5)
Soccer example:
Elements of this game
The players: You and the goalie
The strategies: Kick right or left
The payoff: Payoff matrix

48. Applications of Nash Equilibria The Zero-Sum Game (3 of 5)
Exhibit 13.9 A Zero-Sum Game: Penalty Kicks
Zero-sum game When one player wins, the other loses, so the payoffs sum to zero

49. Applications of Nash Equilibria The Zero-Sum Game (4 of 5)
So what should the penalty kicker and goalie do? Always pick “right” or “left”? Zero-Sum game: strategy randomize

50. Applications of Nash Equilibria The Zero-Sum Game (5 of 5)
Pure strategy Choosing one strategy Mixed strategy Randomly choosing different strategies

51. How Do People Actually Play Such Games?
Does game theory work in the real world?
Two problems:
What are the payoffs?
Players may have different abilities

52. Extensive-Form Games (1 of 2)
Extensive-form games There is an order to play instead of simultaneous play—i.e., one player goes first

53. Extensive-Form Games (2 of 2)
Game tree Representation of an extensive form game

54. Exhibit 13.12 A Game Tree for the Work-or-Surf Game (1 of 2)
What should you do?

55. Exhibit 13.12 A Game Tree for the Work-or-Surf Game (2 of 2)
What should you do?
Gina’s choices are Work or Surf
Both of your payoffs depend on the other’s choice
Your choices are Work or Surf
Wait – highest payoff for surfing? If you surf and Gina works You get profit from the business plus the value of surfing!
The bottom part lists your payoffs if you choose to surf

56. Extensive-Form Games Backward Induction (1 of 4)
Backward induction Considering the last decision and deducing what the previous decisions have been

57. Extensive-Form Games Backward Induction (2 of 4)
Exhibit Panel (a): Gina’s Game Tree If You Decide To Work. Panel (b): Gina’s Game Tree If You Decide To Surf.

58. Extensive-Form Games Backward Induction (3 of 4)
Exhibit Panel (a): Gina’s Game Tree If You Decide To Work. Panel (b): Gina’s Game Tree If You Decide To Surf.

59. Extensive-Form Games Backward Induction (4 of 4)
Gina’s two strategies: Surf if you work (you earn $300) Work if you surf (you earn $500) Since you now know what Gina will do as a result of each of your decisions, you can make the best decision…which is?

60. Extensive-Form Games First-Mover Advantage, Commitment, and Vengeance (1 of 2)
First-mover advantage When the first player in a sequential game benefits from being first

61. Exhibit 13.14 An Extensive-Form Game with a Credible Commitment
Extensive-Form Games First-Mover Advantage, Commitment, and Vengeance (2 of 2)
Exhibit An Extensive-Form Game with a Credible Commitment
Could Gina do something to force us to work instead of surf?

62. Game Theory and Strategic Play (2 of 4)
Evidence-Based Economics Example:
Is there value in putting yourself into someone else’s shoes in extensive form games?

63. Game Theory and Strategic Play (3 of 4)
Exhibit A Trust Game between You and Bernie

64. Game Theory and Strategic Play (4 of 4)
Is this the way we want things to be?

65. Copyright