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1.1 Normal Form Game-exe

# 1.1 Normal Form Game-exe - AMS 335/ECO 355 Game Theory...

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AMS 335/ECO 355 Game Theory Fall 2010 Exercise of 1.1 Normal Form Game Zhen Xu Page 1 of 5 Exercise 1.1.1 the Prisoners’ Dilemma An especially simple description used by Aumann (1987) is the game in which each player can simply announce to a referee: "Give me \$1,000," or "Give the other player \$3,000." Note that the monetary payments come from a third party, not from either of the players; the Prisoner's Dilemma is a variable-sum game. The players can discuss the game in advance but the actual decisions must be independent. The Cooperate strategy is for each person to announce the \$3,000 gift, while the Defect strategy is to take the \$1,000 (and run!). Table 1 below depicts the payoff matrix to the Aumann version of the Prisoner's Dilemma, where the units of the payoff are thousands of dollars. Table 1 The Prisoner's Dilemma Player 2 Cooperate Defect Player 1 Cooperate 3, 3 0, 4 Defect 4, 0 1, 1 We will discuss this game in more detail below, but we should point out the "dilemma" before proceeding. The problem is that each party has an incentive to defect, regardless of what he or she believes the other party will do. If I believe that the other person will cooperate and give me a \$3,000 gift, then I will get \$4,000 in total by defecting. On the other hand, if I believe that the other person will defect and just take the \$1,000, then I do better by taking \$1,000 for myself. The “dilemma” is caused by the existence of dominated and dominant strategy. Note: Cooperate is strictly dominated by Defect. There is no credibility that any players in the game will play Cooperate, or to say, the probability that a player plays Cooperate is 0. Therefore the game can never reach the pareto optimal since Defect is always a better choice for each player.

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1.1 Normal Form Game-exe - AMS 335/ECO 355 Game Theory...

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