5 players must simultaneously choose a number from the interval [0, 9]. Let xi denote the number chosen by player i; x = (x1, . . . , x5) all the selected numbers; x−i = x\xi all the selected numbers except the one chosen by player i. If player i chooses the number xi ∈ [0, 9], while the others choose numbers x−i, then the utility of player i is given by ui(xi, x−i) = 4(9 − xi) + 2Σ5 j=1 xj. Find the Nash equilibrium of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game, obligating them to choose the number 9?
5 players must simultaneously choose a number from the interval [0, 9]. Let xi denote the number chosen by player i; x = (x1, . . . , x5) all the selected numbers; x−i = x\xi all the selected numbers except the one chosen by player i. If player i chooses the number xi ∈ [0, 9], while the others choose numbers x−i, then the utility of player i is given by ui(xi, x−i) = 4(9 − xi) + 2Σ5 j=1 xj. Find the Nash equilibrium of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game, obligating them to choose the number 9?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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5 players must simultaneously choose a number from the interval [0, 9]. Let xi denote the number chosen by player i; x = (x1, . . . , x5) all the selected numbers; x−i = x\xi all the selected numbers except the one chosen by player i. If player i chooses the number xi ∈ [0, 9], while the others choose numbers x−i, then the utility of player i is given by ui(xi, x−i) = 4(9 − xi) + 2Σ5 j=1 xj. Find the Nash equilibrium of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game, obligating them to choose the number 9?
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