Chapter 12 The Theory of Games Introduction

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Chapter 12The Theory of Games Introduction

• Strong or weak pig
• Prisoners Dilemma
• System for studying strategic behavior
• Positive
• Normative

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Game Matrices

• Diagram
• Shows players strategy choices across top
• Other players strategy choices along left side
• Corresponding outcomes in appropriate boxes
• Ex. Pigs in a Box

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Choosing Strategies

• Player choosing columns or rows
• Adjusting choice
• Nash equilibrium
• Neither player chooses to deviate form outcome
• Take other players behavior as given

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Prisoners Dilemma Revisited

• Nash equilibrium
• Pareto optimality
• Dominant strategy
• Player follows strategy regardless of other
  players behavior
• Relationship to Nash equilibrium
• Battle of sexes game
• Copycat game

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Prisoners Dilemma

• Game with 2 players
• Crime committed
• Players must decide how to play game
• Choose best strategy
• Invisible hand does not hold true
• Repeated Prisoners Dilemma
• Tit-for-Tat

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EXHIBIT 12.5 The Battle of the Sexes Revisited
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EXHIBIT 12.6 Pigs in a Box Revisited
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Nash Equilibrium

• Solution concept
• Rule for predicting outcomes
• No or multiple equilibrium situations
• Ex. car insurance
• Pure versus mixed strategy
• Positive concept

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Pareto Optima

• Pareto improvement or preferred outcome
• No one objects to change
• Pareto-optimal outcome
• Outcome where Pareto improvement impossible
• Nash equilibriums not guaranteed Pareto optimal

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Sequential Games

• Simultaneous games
• Second player advantage
• Oligopoly problem
• Stackelberg equilibrium
• Player commits to strategy
• Importance of commitment