Chapter 8: Games and Strategic. . Describe the basic elements of a . Recognize and show the effects of dominant. strategies and dominated . Identify and explain the Prisoners Dilemma and. how it applies to real-world . Explain games in which the timing of players. choices . Discuss strategies that enable players to reap. gains through cooperation McGrawHill/Irwin Copyright © 2011 by The McGrawHill Companies, Inc. All rights reserved. Game Theory.• Basic elements of a game:. – The players. – Their available strategies, actions, or decisions. – The payoff to each player for each possible action.• A dominant strategy is one that yields a higher. payoff no matter what the other player does. – A dominated strategy is any other strategy available. to a player who has a dominant strategy 82 Equilibrium in a Game.• A Nash equilibrium is any combination of. strategies in which each player’s strategy is her. or his best choice, given the other player’s. strategies. – Equilibrium occurs when each player follows his. dominant strategy, if it exists. – Equilibrium does not require a dominant strategy. 83 Prisoner’s Dilemma.• The advertising example illustrates an important. class of games called the prisoner’s dilemma.• The prisoner’s dilemma is a game in which. each player has a dominant strategy, and when. each plays it, the resulting payoffs are smaller. than if each had played a dominated strategy. 84 Prisoners Dilemma. Dominant Optimal. strategy strategy.– Two prisoners are held in separate cells for a serious. crime they did commit.– The prosecutor lacks sufficient evidence. Jaspers Options. Horaces. Confess Dont Confess. Options. Horace: 5 years Horace: 0 . Jasper: 5 years Jasper: 20 years. Horace: 20 years Horace: 1 Confess. Jasper: 0 years Jasper: 1 year. 85 Cartels.• A cartel is a coalition of firms that agree to. restrict output to increase economic profit. – Restrict total output. • Allocate quotas to each player. 86 Repeated Prisoners Dilemma.• In a repeated prisoner’s dilemma the same. players repeatedly face the same prisoner’s. dilemma.• Both players benefit from collaboration. – Tit-for-tat strategy limits defections.• A tit-for-tat strategy says my move in this round. is whatever your move was in the last round. – If you defect, I defect.• Tit-for-tat is rarely observed in the market. – This strategy breaks down with more than two. players or potential players. 87 Sometimes Timing Matters.• One party moves first. – The second can adjust his strategy accordingly.• Viper and Corvette hybrid models. – When timing does not matter, the payoff matrix. shows no dominant strategy.• When timing matters a decision tree is a more. useful way of representing payoffs. – A decision tree describes the possible moves in a. game in sequence. – A decision tree is sometimes called a game tree 88 Simultaneous Decisions. Dodge Vipers Corvettes. Hybrid No Hybrid. Options. Chevy: $60 M Chevy: $80 . Dodge: $60 M Dodge: $70 M. Chevy: $70 M
