= - Five players must simultaneously choose a number from the interval [0, 9]. Let x; denote the number chosen by player i; x = (x1, ..., x5 ) all selected numbers; x_{ x\x; all selected numbers except the number chosen by player i. If player i chooses the number x; Є [0,9], while the others choose the numbers _, then the utility of player i is u; (xi, x_i) = 4(9 − xi) + 2-1 xj. Find the Nash equilibria of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game requiring them to choose the number 9?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Question
=
-
Five players must simultaneously choose a number from the interval [0, 9]. Let x; denote the
number chosen by player i; x = (x1, ..., x5 ) all selected numbers; x_{ x\x; all selected
numbers except the number chosen by player i. If player i chooses the number x; Є [0,9], while
the others choose the numbers _, then the utility of player i is u; (xi, x_i) = 4(9 − xi) +
2-1 xj. Find the Nash equilibria of the game and the corresponding utilities. Would all players
be better off if they signed a binding contract before the game requiring them to choose the
number 9?
Transcribed Image Text:= - Five players must simultaneously choose a number from the interval [0, 9]. Let x; denote the number chosen by player i; x = (x1, ..., x5 ) all selected numbers; x_{ x\x; all selected numbers except the number chosen by player i. If player i chooses the number x; Є [0,9], while the others choose the numbers _, then the utility of player i is u; (xi, x_i) = 4(9 − xi) + 2-1 xj. Find the Nash equilibria of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game requiring them to choose the number 9?
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