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Homework answers / question archive /  a game tree that represents the ultimatum game in which the proposer is a first mover who decides how much to offer a responder and the responder then decides to accept or reject the offer

 a game tree that represents the ultimatum game in which the proposer is a first mover who decides how much to offer a responder and the responder then decides to accept or reject the offer

Economics

 a game tree that represents the ultimatum game in which the proposer is a first mover who decides how much to offer a responder and the responder then decides to accept or reject the offer. The total amount available is $50 if agreement is reached but both players get nothing if the responder rejects the offer. Accept Assume for simplicity the game tree is illustrated in the figure to the right, where the proposer is player 1, the responder is player 2, and player 1 may offer $0.01 or offer to divide the sum equally (offer $25.00). Player 1's payoffs are the first listed, and player 2's payoffs are the second listed. What is the subgame perfect Nash equilibrium? (49.99, 0.01) Player 2 Offer $0.01 (0.00, 0.00) Reject Player 1 Accept A. The game does not have a Nash equilibrium. B. The Nash equilibrium is for the proposer to offer $25.00 and the responder to accept any positive offer. C. The Nash equilibrium is for the proposer to offer $0.01 and the responder to reject all offers. D. The Nash equilibrium is for the proposer to offer $0.01 and the responder to accept any positive offer. E. The Nash equilibrium is for the proposer to offer $0.01 and the responder to accept only offers of $25.00 or more. (25.00, 25.00) Offer $25.00 Player 2 -(0.00, 0.00) Reject

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Answer:

D. The Nash equilibrium is for the proposer to offer $0.01 and the responder to accept any positive offer.

reason: Before making the offer, Player 1 checks Player 2's response. If Player 1 offers $25, Player 2 will accept it as he will get 0 if he does not accept (25>0). If he offers $0.01, Player 2 will accept it as he will get nothing if he does not accept (0.01 > 0). Between these two responses of Player 2, Player 1 gains more with the first option. So he offers $0.01 knowing that Player 2 will accept it and he himself will get a payoff of $49.99.