please only do: if you can teach explain each part ing. In the first round, player 1 proposes a division x = (₁, 2, 3), with x₁ + x2 + x3 = 1.After observing the proposed x, first player 2 chooses whether to accept or reject it, thenplayer 3 does. If both accept the proposal, it is implemented and each player i receives payoffxį. If either rejects the proposal, then we move to the second round of bargaining, in whichplayer 2 proposes a division y = (y₁, 92, Y3) with y₁ + y2 + y3 = 1, which player 3 first decideswhether to accept or reject, followed by player 1. If both 3 and 1 accept, the proposal isimplemented, and each player i receives payoff dy;, where & € (0, 1) is a common discountfactor. If either rejects the proposal, we move to the third round, in which player 3 makesa proposal z = (2₁, 22, 23) with 21 + 22 + z3 = 1 that player 1 accepts or rejects, followed byplayer 2. If both 1 and 2 accept, each player i receives payoff 62%i, whereas if either rejects,all players receive payoffs of 0.(a) Find all subgame perfect equilibrium outcomes of this game. (Note that you do not haveto describe the full equilibrium strategies.)Solution: Proceed by backward induction. By the same logic as in the Ultimatum Game,the subgame beginning with Player 3's proposal in the third round has a unique SPE givenby z = (0, 0, 1) and the other players accepting all offers. Given this, in the second round,Player 1 will accept any offer and Player 3 will accept any offer of at least 6. Player 2will therefore offer y = (0, 18, 6). Given this, in the first round, Player 2 will acceptany offer of at least 8(1-5) and Player 3 will accept any offer of at least 62. Thus thereis a unique SPE outcome, which involves Player 1 offering x = (1-8, 8(1-6), 5²) andboth other players accepting.

The ultimatum game is the bargaining game in which the proposer proposes the offer and the responder…

ing. In the first round, player 1 proposes a division x = (1, 2, 3), with x₁ + x2 + x3 = 1. After observing the proposed x, first player 2 chooses whether to accept or reject it, then player 3 does. If both accept the proposal, it is implemented and each player i receives payoff ₁. If either rejects the proposal, then we move to the second round of bargaining, in which player 2 proposes a division y = (y1, 92, 93) with y₁ + y2 + y3 = 1, which player 3 first decides whether to accept or reject, followed by player 1. If both 3 and 1 accept, the proposal is implemented, and each player i receives payoff dyi, where & € (0, 1) is a common discount factor. If either rejects the proposal, we move to the third round, in which player 3 makes

ing. In the first round, player 1 proposes a division x = (1, 2, 3), with x₁ + x2 + x3 = 1. After observing the proposed x, first player 2 chooses whether to accept or reject it, then player 3 does. If both accept the proposal, it is implemented and each player i receives payoff ₁. If either rejects the proposal, then we move to the second round of bargaining, in which player 2 proposes a division y = (y1, 92, 93) with y₁ + y2 + y3 = 1, which player 3 first decides whether to accept or reject, followed by player 1. If both 3 and 1 accept, the proposal is implemented, and each player i receives payoff dyi, where & € (0, 1) is a common discount factor. If either rejects the proposal, we move to the third round, in which player 3 makes

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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