Consider the following bargaining game in which two players are trying to share a cake of...

 

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Consider the following bargaining game in which two players are trying to share a cake of size a > 0. Player 1 offers 2₁ € [0, a] and player 2 either accepts (Y) or rejects (N). If player 2 accepts, then player 1 receives a payoff ₁ and player 2 receives a- ₁. If player 2 rejects, then player 2 moves again to offer 12 € [0, a] and now player 1 either accepts (Y) or rejects (N). If player 1 accepts, then player 2 receives a payoff d2 and player 1 receives (a - x2), where & € (0,1) is the common discount factor for the players. If player 1 rejects the offer, then an arbitrator terminates the bargaining process and gives player 1 a share y = [0, a] and player 2 the rest which, because of discounting, players value as 62y and 62(a - y), respectively. Assume that each player accepts an offer if s/he is indifferent. Fine all subgame perfect Nash equilibria. Consider the following bargaining game in which two players are trying to share a cake of size a > 0. Player 1 offers 2₁ € [0, a] and player 2 either accepts (Y) or rejects (N). If player 2 accepts, then player 1 receives a payoff ₁ and player 2 receives a- ₁. If player 2 rejects, then player 2 moves again to offer 12 € [0, a] and now player 1 either accepts (Y) or rejects (N). If player 1 accepts, then player 2 receives a payoff d2 and player 1 receives (a - x2), where & € (0,1) is the common discount factor for the players. If player 1 rejects the offer, then an arbitrator terminates the bargaining process and gives player 1 a share y = [0, a] and player 2 the rest which, because of discounting, players value as 62y and 62(a - y), respectively. Assume that each player accepts an offer if s/he is indifferent. Fine all subgame perfect Nash equilibria.

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Lets break this game down backwards from its last possible subgame following the principles of subga... View the full answer