Players 1, 2, and 3 are playing a game in which the strategy of player i isdenoted yi and can be any nonnegative real number. The payoff function for player 1 is V1(y1,y2,y3) = y1 + y1y2 - (y1)2,for player 2 is V2(y1,y2,y3) = y2 + y1y2 - (y2)2,and for player 3 is V3(y1,y2,y3) = (10 - y1 - y2 - y3)y3.These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: Thepayoff functions are symmetric for players 1 and 2.)

Considering the payoff functions for all the players: For player 1: V1 = y1+y1y2-y12∂V1∂y1 =…

Answered: Players 1, 2, and 3 are playing a 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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Players 1, 2, and 3 are playing a game in which the strategy of player i is
denoted yi and can be any nonnegative real number. The payoff function for player 1 is
V₁(y₁,y₂,y₃) = y₁+ y₁y₂ - (y₁)²,
for player 2 is
V₂(y₁,y₂,y₃) = y₂+ y₁y₂ - (y₂)²,
and for player 3 is
V₃(y₁,y₂,y₃) = (10 - y₁ - y₂ - y₃)y₃.
These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: The
payoff functions are symmetric for players 1 and 2.)

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