Game Theory and Strategic Play Microeconomics Second Edition Chapter 13 Game Theory and Strategic Play If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed: 1) MathType Plugin 2) Math Player (free versions available) 3) NVDA Reader (free versions available)

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

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.

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.

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?

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?

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

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

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…

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.

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

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

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

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?

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?

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

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)

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?

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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?

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?

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?

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?

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?

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

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?

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?

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?

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

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

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

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

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?

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!

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

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

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

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

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

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

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

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

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

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

Extensive-Form Games Backward Induction (2 of 4) Exhibit 13.13 Panel (a): Gina’s Game Tree If You Decide To Work. Panel (b): Gina’s Game Tree If You Decide To Surf.

Extensive-Form Games Backward Induction (3 of 4) Exhibit 13.13 Panel (a): Gina’s Game Tree If You Decide To Work. Panel (b): Gina’s Game Tree If You Decide To Surf.

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?

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

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

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?

Game Theory and Strategic Play (3 of 4) Exhibit 13.15 A Trust Game between You and Bernie

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

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