We examine innovation as a timing game with complete information and observable actions in which firms decide when to enter a market. We characterize all pure strategy subgame perfect equilibria for the two-player symmetric game. In particular, we describe all subgame perfect equilibria when both the leader's and the followers' payoff functions are multi-peaked, non-monotonic and discontinuous. We find that there are potentially multiple equilibria, which could involve: joint adoption by both firms, with and without rent equalization; and, alternatively, single-firm adoption with a second-mover advantage. Economic applications are discussed including process and product innovation and the timing of the sale of an asset.