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.