The game pictured below is called the centipede game. AAA A-100 98 97 99 98 98 1

Question

The game pictured below is called the centipede game. AAA A-100 98 97 99 98 98 100 99 101 3 where all nodes marked 1 denote a decision by player 1 and all nodes marked 2 denote a decision by player 2. a) Show, by backward induction, that rational players choose d at every node of the game, yielding a payoff of 1 for Player 1 and a payoff of 1 for Player 2. Obviously, you do not need to go through all 100 subgames; just reason through the process. b) Explain why this equilibrium seems reasonable or unreasonable in real life. c) What rationality assumptions lead to this reasonable/unreasonable Nash equilibrium.

Explanation / Answer

a) By backward induction, comparing the different payoffs of the players at each stage starting from the last stage shows, defection is the unique subgame perfect equilibrium of the extensive game which can be affirmed by using backward induction.

b) Like a prisoner's dilemma, this game shows a conflict between self-interest and mutual benefit. It was enforced both players would prefer to cooperate but if there is distrust or self-interest creates a situation where both players do worse than if cooperate blindly. It is related to a real life scenario where the exchange of goods between parties creates distrust.

c) assumption of bounded rationality leads to a reasonable nash equilibrium.

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