Consider the following two-player game. First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously and independently, player 1 selects a number y1 and player 2 selects a number y2, at which point the game ends. Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8x Player 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2 Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.

Consider the following two-player game. First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously and independently, player 1 selects a number y1 and player 2 selects a number y2, at which point the game ends. Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8x Player 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2 Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

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