ch14_Solutions

# ch14_Solutions - Chapter 14 Game Theory and Strategic...

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Chapter 14 Game Theory and Strategic Behavior Solutions to Review Questions 1. A Nash equilibrium in a game occurs when each player chooses a strategy that gives it the highest payoff, given the strategies chosen by the other players in the game. If players chose strategies that did not constitute a Nash equilibrium, then the players could choose another strategy that increased their payoff given the strategies chosen by the other players. Since players could increase their payoffs by choosing other strategies, strategies that do not constitute a Nash equilibrium are an unlikely outcome in a game. 2. A prisoners’ dilemma game illustrates the conflict between self-interest and collective-interest. In the Nash equilibrium of a prisoners’ dilemma game, each player chooses a non-cooperative action even though it is in the players’ collective interest to pursue a cooperative action. No, not every game in the chapter is a prisoners’ dilemma. For example, the game of Chicken presented in Table 14.7 is not a prisoners’ dilemma. 3. A dominant strategy is a strategy that is better than any other strategy the player might follow no matter what the other player does. A player has a dominated strategy when it has other strategies that give it a higher payoff no matter what the other player does. A player would be unlikely to choose a dominated strategy because the player could always improve his payoff by choosing another strategy regardless of the strategies chosen by the other players. 4. The Chicken game is special because it has multiple Nash equilibria. In each Nash equilibria, one player chooses a cooperative strategy (Swerve) while the other player chooses a non-cooperative strategy (Stay). There are multiple equilibria in this game because it is uncertain at the outset which player will Swerve and which will Stay. This game differs from the prisoners’ dilemma. In the prisoners’ dilemma, both players have a dominant strategy to confess, and by choosing this dominant strategy, both players receive a payoff worse than if they both chose to not confess. 5. Yes, a game can have a Nash equilibrium even though neither player has a dominant or dominated strategy. In fact, every game has a Nash equilibrium, Page 14 - 1

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possibly in mixed strategies. The game of Chicken is an example of a game with no dominant or dominated strategies but which has a Nash equilibrium. 6. A pure strategy is a specific choice of strategy among the possible moves a player may choose in a game. With a mixed strategy, a player chooses among two or more pure strategies according to pre-specified probabilities. 7. In the repeated prisoners’ dilemma game, the players might, in equilibrium, play cooperatively. This could occur if one player chose to cooperate with the other player as long as the other player chose to cooperate and to resort to non- cooperation when the other player cheated. For this to work, the short-term benefit of cheating must be lower than the long-term benefit of not cheating. This
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## This homework help was uploaded on 02/19/2009 for the course PAM 2000 taught by Professor Evans,t. during the Fall '07 term at Cornell University (Engineering School).

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ch14_Solutions - Chapter 14 Game Theory and Strategic...

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