4. Consider a three-player bargaining, where the players are negotiating over a surplus of one unit of utility. The game begins with player 1 proposing a three-way split of the surplus. Then player 2 must decide whether to accept the proposal or to substitute for player 1's proposal his own alternative proposal. Finally, player 3 must decide whether to accept or reject current proposal (it is player 1's if player 2 accepts or player 2's if player 2 offer a new one). If he accepts, then the players obtain the specified shares of the surplus. If player 3 rejects, then the players each get 0. (a) Draw the extensive form game of this perfect-information game. (b) Determine the subgame perfect NE.

4. Consider a three-player bargaining, where the players are negotiating over a surplus of one unit of utility. The game begins with player 1 proposing a three-way split of the surplus. Then player 2 must decide whether to accept the proposal or to substitute for player 1's proposal his own alternative proposal. Finally, player 3 must decide whether to accept or reject current proposal (it is player 1's if player 2 accepts or player 2's if player 2 offer a new one). If he accepts, then the players obtain the specified shares of the surplus. If player 3 rejects, then the players each get 0. (a) Draw the extensive form game of this perfect-information game. (b) Determine the subgame perfect NE.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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2 Consider Anna and Joe, who value a certain good by the same amount v and can choose to either contribute (C) e to get the good or not (N) where v > e> 0. Obtaining the good only requires c from one person. The game is summarized in the payoff table below: Joe V-c,V-c V-c,V v,V-c 0,0 Find a pure strategy equilibrium and a mixed strategy equilibrium. Anna O Z
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