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 for a leader's payofffunctions to be multi-peaked and non-monotonic, only requiring that followers' payoffs are non-increasing with the time of the leader's entry. We provide conditions for when equilibrium actions do not depend on historic payoffs, showing in this case that the $n$-player asymmetric game generates standard leader-maximized or preemption equilibria. In the two-player game we provide a complete characterization of the pure-strategy equilibria for when historic payoffs affect equilibrium actions (including the possibility of no equilibria in pure strategies). Finally, we relate our results to three applications from the literature