chapter 12 choices involving strategy copyright © 2014 mcgraw-hill education. all rights reserved....
TRANSCRIPT
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)
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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
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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
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12-6
Describing a Game
• One-stage games:1) Identify the players and list the strategies available to
each2) Identify each player’s payoff for every possible
combination of strategies
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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
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12-8
Prisoners’ Dilemma
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Best Responses in the Prisoners’ Dilemma
12-9Copyright © 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
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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 them3. Repeat this process until there are no more dominated
strategies left to remove
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12-12
Iterative Deletion of Dominated Strategies in the Provost’s Nephew
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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
12-13Copyright © 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
12-14Copyright © 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
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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
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12-17
Best Responses
20
15
10
5
0 5 10 15 20
Scott’s best response
Liz’s best response
Liz’s
hou
rs
Scott’s hours
7
CA
B
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12-18
Nash Equilibrium
20
15
10
5
0 5 10 15 20
Scott’s best response
Liz’s best response
Liz’s
hou
rs
Scott’s hours
N8
8
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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
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12-20
No Nash Equilibrium in Pure Strategies
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Describing a Game with Perfect Information
• Perfect information: players make their choices one at a time and nothing is hidden from any player
12-21Copyright © 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
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12-23
Solving by Backward Induction
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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
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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
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12-26
Spouses’ Dilemma
One-shot equilibrium: Homer: loaf
Marge: loaf
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12-27
Repeated Game: An Equilibrium Without Cooperation
• Only Nash equilibrium if game is finitely repeated– Homer: always loaf– Marge: always loaf
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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)
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12-29
Games in Which Different People Have Different Information
• Categories:1) Imperfect information: objective information is
available to one party, but not to another2) 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
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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
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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
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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
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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.
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