A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x i in the interval [ 0 , 1 ] , and a player's payoff is the distance from its point x i to the next larger point, or to 1 if x i is the largest. For this game, we giv...

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Bibliographic Details
Published in:Games and economic behavior 2008-03, Vol.62 (2), p.643-660
Main Authors: Lotker, Zvi, Patt-Shamir, Boaz, Tuttle, Mark R.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational methods
Differential equations
Equilibrium
Game theory
Nash equilibrium
Pay-off
Studies
Time
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Summary:We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x i in the interval [ 0 , 1 ] , and a player's payoff is the distance from its point x i to the next larger point, or to 1 if x i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2007.04.006