Competitive influence maximization in social networks
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
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We consider the following abstraction of competing publications. There are n players vying for the attention of the audience. The attention of the audience is abstracted by a single slot which holds, at any given time, the name of the latest release. Each player needs to choose, ahead of time, when to release its product, and the goal is to maximize the amount of time its product is the latest release. Formally, each player i chooses a point xi ∈ [0,1], and its 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, continuous-action 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-action 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.