Consider the version of the location game defined by the following payoff functions: U₁(x1, x2) 1- [0.25][x1 - 012 - [0.75][x2-x11², U₂(x1, x2) = 1 [0.2][1-x212 [0.8][x2 - x11². Here each player i = 1,2 chooses their own location x, E [0, 1] and receives payoff U/(x1, x2). Instead of the players' choices being game-theoretically simultaneous, suppose that player 2 chooses her location first and player 1 chooses his locatic Moreover, suppose that player 1 observes the choice of x2 before choosing x₁. This game has a unique subgame perfect Nash equilibrium in which player 2's choice of location is x*.

Consider the version of the location game defined by the following payoff functions: U₁(x1, x2) 1- [0.25][x1 - 012 - [0.75][x2-x11², U₂(x1, x2) = 1 [0.2][1-x212 [0.8][x2 - x11². Here each player i = 1,2 chooses their own location x, E [0, 1] and receives payoff U/(x1, x2). Instead of the players' choices being game-theoretically simultaneous, suppose that player 2 chooses her location first and player 1 chooses his locatic Moreover, suppose that player 1 observes the choice of x2 before choosing x₁. This game has a unique subgame perfect Nash equilibrium in which player 2's choice of location is x*.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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