The game pictured below is called the centipede game 2 A 100 100 98 98 97 100 99
ID: 1132191 • Letter: T
Question
The game pictured below is called the centipede game 2 A 100 100 98 98 97 100 99 98 101 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 equilibriumExplanation / Answer
a) The reasoning goes like this. For a game that ends after four rounds, this reasoning proceeds as follows. If we were to reach the last round of the game, Player 2 would do better by choosing D instead of A, receiving 101 instead of 100. However, given that 2 will choose D, 1 should choose D in the second to last round, receiving 99 instead of 98. Given that 1 would choose D in the second to last round, 2 should choose D in the third to last round, receiving 100 instead of 99. But given this, Player 1 should choose D in the first round, receiving 98 instead of 97.
Like this, we can argue for a game with 100 rounds. Hence the sub-game perfect nash equilibrium will be one where each player chooses D whenever he/she has asked to move.
b) This equilibrium is unreasonable because, in real life, this equilibrium is rarely observed. Because participants usually partially cooperate for a few initial rounds by choosing A, before they choose D. This happens because some of the participants could be altruistic.
c) This unreasonable equilibrium assumes that people are selfish, they are not altruistic. They only care about their profits/payoffs. That is while taking decisions they care about their own payoffs only.
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