Analysis of strategic behavior in the centipede game
For the purposes of this essay, the centipede game is described as follows: The centipede game is a famous finite game of perfect information. In this game two players move sequentially one after another. At the beginning of the game, player 1 can either terminate the game immediately (in which case both players receive a small payoff of 1) or pass the move to player 2. Player 2 can then either terminate the game (in which case player 1 receives nothing and player 2 receives a payoff of 2) or pass the move back to player 1. Player 1 can then either terminate the game (in which case both players receive a payoff of 2) or pass the move back to player 2. The game continues in this fashion for many rounds with payoffs gradually increasing. If the last round is reached, player 2 must decide between option R where both players receive a payoff of 100 and option D where player 1 receives a payoff of 98 and player 2 receives a payoff of 101.
The centipede game is presented in the extensive form on Figure below.
1.Describe a unique subgame perfect Nash equilibrium of the centipede game
2.Discuss why such Nash equilibrium appears counterintuitive
3.Using your practical understanding of strategic thinking describe the most reasonable prediction for the game
4.Using your theoretical understanding of strategic thinking , discuss how such most reasonable prediction can be rationalized/explained; DO NOT forget that both players behave strategically in the game