chapter 12 Choices Involving Strategy Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-2 Learning Objectives Explain what an economist means by a game, and distinguish between one-stage and multiple-stage games. Describe and apply methods for reasoning out likely strategic choices. Explain the concept of a Nash equilibrium, and apply it in simple games. Understand the benefits of playing unpredictably in certain types of games. Recognize whether threats are credible, and whether cooperation is achievable, in multiple-stage games. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-3 Overview Strategic decisions play a role when the effects of your actions depend on the actions and reactions of other people Game theory is the tool economists use to analyze strategic situations Strategic situations can be over after one set of decisions (one-stage games) or may involve a sequence of decisions (multiple-stage games) Just as competitive markets have equilibria, strategic games have Nash equilibria Sometimes all participants (players) in a game have access to the same information, but sometimes different people have different information (asymmetric information) Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-4 What is a Game? Game: a situation in which a number of individuals make decisions, and each cares both about his own choice and about others’ choices Example: game theory provides the foundation for understanding competition in industries with only a few producers Example: every negotiation is a game Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-5 Two Types of Games One-stage game: each participant makes all of their choices before observing any choice by any other participant Multiple-stage game: at least one participant observes a choice by another participant before making some decision Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-6 Describing a Game One-stage games: 1)Identify the players and list the strategies available to each 2)Identify each player’s payoff for every possible combination of strategies Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-7 Strategy Concepts Best response: a strategy that provides player with the highest possible payoff, assuming other players behave in a specified way Dominant strategy: a player’s only best response, regardless of other players’ choices – When a player has a dominant strategy, she does not need to think about what other players will do Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-8 Prisoners’ Dilemma Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Best Responses in the Prisoners’ Dilemma 12-9 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-10 Equilibrium in the Prisoner’s Dilemma Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-11 Dominated Strategies Dominated strategy: if there is some other strategy that yields a strictly higher payoff regardless of others’ choices Iterative deletion of dominated strategies: the process of removing the dominated strategies from a game, resulting in a simplified game 1.Remove the dominated strategies from a game 2.Inspect the simplified game to determine whether it contains any (new) dominated strategies. If it does, remove them 3.Repeat this process until there are no more dominated strategies left to remove Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-12 Iterative Deletion of Dominated Strategies in the Provost’s Nephew Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Weakly Dominated Strategy Weakly dominated strategy: if there is some other strategy that yields a strictly higher payoff in some circumstances, and that never yields a lower payoff regardless of others’ choices Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Nash Equilibrium in the Prisoners’ Dilemma Nash equilibrium: the strategy played by each individual is a best response to the strategies played by everyone else Nash equilibrium payoffs Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-15 Justifications for Nash Equilibrium Why would we expect a group of people to settle on a stable combination of strategies? When people play games repeatedly, they gain experience and learn how others tend to play. If all players eventually learn to make accurate guesses, they will all play best responses to their opponents’ actual decisions, effectively playing a Nash equilibrium. Self-enforcing agreement: every party to the agreement has an incentive to abide by it, assuming others do the same Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-16 Nash Equilibria in Games with Finely Divisible Choices Best response function or reaction function: shows the relationship between one player’s choice and the other’s best response Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-17 Best Responses Scott’s best response Liz’s best response Liz’s hours Scott’s hours 7 C A B Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-18 Nash Equilibrium Scott’s best response Liz’s best response Liz’s hours Scott’s hours N 8 8 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-19 Playing Unpredictably Pure strategy: when a player chooses a strategy without randomizing Mixed strategy: when a player uses a rule to randomize over the choice of a strategy Mixed strategy equilibrium: players choose mixed strategies, and the mixed strategy chosen by each is a best response to the mixed strategies chosen by the others Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-20 No Nash Equilibrium in Pure Strategies Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Describing a Game with Perfect Information Perfect information: players make their choices one at a time and nothing is hidden from any player Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-22 Thinking Strategically in a Game with Perfect Information Backward induction: the process of solving a strategic problem by reasoning in reverse, starting at the end of the tree diagram that represents the game, and working back to the beginning Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-23 Solving by Backward Induction Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-24 Tony’s and Maria’s Nash Equilibrium Tony’s strategy: choose the action-adventure film Maria’s strategy: – if Tony chooses the action-adventure film, then choose the action-adventure film – if Tony chooses the romantic comedy, then choose the romantic comedy Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-25 Cooperation in Repeated Games Repeated game: formed by playing a simpler game many times in succession Finitely repeated game: formed by repeating a simpler game a fixed number of times Infinitely repeated game: formed by repeating a simpler game indefinitely Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-26 Spouses’ Dilemma One-shot equilibrium: Homer: loaf Marge: loaf Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-27 Repeated Game: An Equilibrium Without Cooperation Only Nash equilibrium if game is finitely repeated – Homer: always loaf – Marge: always loaf Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-28 Repeated Game: Equilibria with Cooperation If this game is infinitely repeated, and Homer and Marge care enough about the future, different equilibria can be reached Grim strategies: permanent punishment for selfish behavior Example of grim strategies: – Homer: clean on the first day. On subsequent days, clean as long as my spouse and I have an unbroken history of cleaning on every previous day; otherwise, loaf. – Marge: (same strategy as Homer’s) Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-29 Games in Which Different People Have Different Information Categories: 1)Imperfect information: objective information is available to one party, but not to another 2)Incomplete information: at least one party is uncertain about another’s preferences, and consequently its objectives Each participant in a game can potentially learn important information from the behavior of other participants When a participant knows that others are trying to learn from his choices, he may have an incentive to mislead others by acting contrary to his immediate interests Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-30 Winner’s Curse Winner’s curse: the tendency, in certain types of auctions, for unsophisticated bidders to overpay whenever they win Potentially arises whenever the item’s commonly perceived value depends on information that may become available to some but not all bidders Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-31 Reputation Reputation: a widely held belief about a characteristic of a person or company that predisposes them to act in a particular way. Usually acquired through patterns of behavior Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-32 Review A game is a situation in which individuals make decisions, and each cares about his own choice and about others’ choices In a Nash equilibrium the strategy played by each individual is a best response to the strategies played by everyone else Nash equilibria are self-enforcing agreements – where every party to the agreement has an incentive to abide by it Economists can analyze not only games with perfect information, but also more realistic scenarios with imperfect or incomplete information Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

12-33 Looking Forward Game theory frequently assumes that people are perfectly rational. Next, we will discuss what happens when people do not behave rationally, an area studied by behavioral economists. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.