General timing games with multiple players

We examine innovation in an n-player market-entry timing game with complete information and observable actions. In our novel multi-player setup, we allow for heterogeneous payoffs between players and leader payoff functions to be multi-peaked and non-monotonic, only requiring that followers’ payoffs are non-increasing with the time of the leader’s entry. We outline the conditions under which an n-player asymmetric game leads to standard second-mover advantage and preemption equilibria. In the context of a two-player game, we provide a comprehensive characterization of the pure-strategy equilibria for a general case. This includes the potential for the emergence of a new type of preemption equilibrium, as well as scenarios where no equilibria in pure strategies exist. Finally, we connect our findings to various applications, offering a new explanation for entry clustering among heterogeneous players