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 xi in the interval [0, 1], and a player’s payoff is the distance from its point xi to the next larger point, or to 1 if xi 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. An extended abstract of this work appeared in 18th ACM Symposium on Parallelism in Algorithms and Architectures, July 2006. Contact author. Postal address: Dept. of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.