Agenda Setting: An agenda-setting game is described as follows. The “issue space" (set of possible policies) is an interval X = [0, 5]. An agenda setter (player 1) proposes an alternative x e X against the status quo q = 4. After player 1 proposes x, the legislator (player 2) observes the proposal and selects between the proposal x and the status quo q. Player l's most-preferred policy is 1, and for any final policy y e X his payoff is given by vy(y) = 10 – ly – 1. where [y – 1| denotes the absolute value of (y – 1). Player 2's most preferred policy is 3, and for any final policy y e X his payoff is given by vz(y) = 10 – ly – 31. That is, each player prefers policies that are closer to his most-preferred policy. a. Write the game down as a normal-form game. Is this a game of perfect or imperfect information? b. Find a subgame-perfect equilibrium for this game. Is it unique? c. Find a Nash equilibrium that is not subgame perfect. Is it unique? If yes, explain. If not, show all the Nash equilibria for this game.

Agenda Setting: An agenda-setting game is described as follows. The “issue space" (set of possible policies) is an interval X = [0, 5]. An agenda setter (player 1) proposes an alternative x e X against the status quo q = 4. After player 1 proposes x, the legislator (player 2) observes the proposal and selects between the proposal x and the status quo q. Player l's most-preferred policy is 1, and for any final policy y e X his payoff is given by vy(y) = 10 – ly – 1. where [y – 1| denotes the absolute value of (y – 1). Player 2's most preferred policy is 3, and for any final policy y e X his payoff is given by vz(y) = 10 – ly – 31. That is, each player prefers policies that are closer to his most-preferred policy. a. Write the game down as a normal-form game. Is this a game of perfect or imperfect information? b. Find a subgame-perfect equilibrium for this game. Is it unique? c. Find a Nash equilibrium that is not subgame perfect. Is it unique? If yes, explain. If not, show all the Nash equilibria for this game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.12P

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