AbstractThe aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (Games and Economic Behavior, 1990, 2, pp. 29–46) by allowing the payoff or the marginal payoff of a player to become non‐monotonic with respect to the strategy of the opponent. We propose a taxonomy of the subgame‐perfect Nash equilibria based on the characteristics of the payoff functions proposed by Eaton (Canadian Journal of Economics, 2004, 37, pp. 805–29). We determine under which conditions of the initial payoff functions commitment has a social value and when the simultaneous‐move Nash equilibrium is commitment robust and discuss its Pareto efficiency.