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Imagine a game in which players 1 and 2 simultaneously and independently select A or B. If they both select A, then the game ends and the payoff vector is (5, 5). If they both select B, then the game ends with the payoff vector (-1, -1). If one of the players chooses A while the other selects B, then the game continues and the players are required simultaneously and independently to select positive numbers. After these decisions, the game ends and each player receives the payoff where x1 is the positive number chosen by player 1 and x2 is the positive number chosen by player 2.
(a) Describe the strategy spaces of the players.
(b) Compute the Nash equilibria of this game.
(c) Determine the subgame perfect equilibria
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This question delves into the Rationalization strategy of Game Theory. If two or more players are playing a game simultaneously as well as individually, they would want to maximum their payoff by taking all options of possible number that the opponent could make. A perfectly rational player would assume the opponent to be perfectly rational as well and think that he will pick what is best payoff giving for him.
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