Find the backward induction solution of the game

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Reference no: EM13154920

Consider the Tragedy of Commons game from the class. Suppose that now, instead of farmers choosing their actions simultaneously, player 1 chooses his action q1 first, then player 2 observes this choice and chooses q2, after which the game ends (and payoffs are as we had them in class). For any q1, find the best response by player 2. Find the Backward Induction solution of this game. What are the payoffs to the players? Suppose now that before the sequential game that we just described player 1 can buy off the property rights to the field from player 2. and so become the sole owner of the field (in which case he chooses qi = 50 and earns 2500). More specifically, consider the extensive form game where in the first round player 1 makes an offer t between 0 and 1500 that is a multiple of 100 (and so has 16 actions available, t = 0, 100, ..., 1500). In the second round, player 2 can either accept or reject. If player 2 accepts t, the game ends with payoffs 2500 - t and t, respectively. If player 2 rejects the offer, players play the extensive game as above (with player 1 chosing q1 in round 3. followed by the choice of q2 by player 2 in round 4). Find the Backward Induction solution of the game. (extra - not graded!) How would the answer change if we reversed the roles of player 1 and 2 in the first two rounds of the game in c)?

Reference no: EM13154920

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