23.03.2023 - 23:14

Solve all NE of the centipede game. Are there NE that are not SPNE? Are there NE where one of the players decides to go forward at the first node?

Question:

Solve all NE of the centipede game. Are there NE that are not SPNE? Are there NE where one of the players decides to go forward at the first node?

Answers (1)
  • Wanda
    April 13, 2023 в 13:45
    The NE (Nash Equilibrium) of the centipede game can be found by working backwards from the final node to the initial node, and selecting the action that maximizes payoff for each player. There are many NE in the game, and all of them involve both players alternating their decisions at each node. However, not all NE are SPNE (Subgame Perfect Nash Equilibrium). A SPNE requires that the NE be played at each subgame of the overall game, which means that the NE must also be optimal for each smaller game within the larger game. There are some NE in the centipede game that are not SPNE because they result in suboptimal outcomes for one or both players in smaller games within the overall game. Regarding the question of whether there are NE where one of the players decides to go forward at the first node, the answer is no. This is because if one player decides to go forward at the first node, they will receive a low payoff, and the other player will receive a high payoff. This means that the second player will continue to go forward at the next node, and the first player will receive an even lower payoff if they follow suit. Therefore, the NE always involve both players alternating their decisions at each node.
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