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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Player 2 Middle Left P1: $45 P1: $70 Up P2: $45 P2: $50 Player 1 P1: $50 P1: $60 Middle P2: $50 P2: $60 P1: $60 P1: $50 Down P2: $60 P2: $70 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, left) (up, middle) (up, right) (middle, left) (middle, middle) (middle, right) (down, left) (down, middle) (down, right) No equilibrium Right P1: $45 P2: $60 P1: $50 P2: $70 P1: $60 P2: $60
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