Multiplicity and Uniqueness of Equilibria in Continuous-Time Dynamic Discrete Games

We consider multiplicity and uniqueness of equilibria in continuous-time dynamic discrete games where players move sequentially according to independent Poisson processes. With multiple equilibria, the structural model is incomplete: the reduced form and counterfactual predictions depend on how equilibria are selected. We provide closed-form sufficient conditions for uniqueness of Markov perfect equilibrium in this class of games. The conditions are semiparametric and can be verified from model primitives. To measure the coverage of the conditions and characterize multiplicity more broadly, we carry out a large-scale numerical search for equilibria of a dynamic duopoly model of entry and exit. Although uniqueness is the norm in our broad search, we find that multiplicity concentrates in economically relevant regions: where the market cannot profitably sustain both firms, where firms are very patient, and at intermediate decision frequencies that balance strategic interaction and commitment. When multiplicity is present, we typically find two stable asymmetric equilibria and one unstable symmetric equilibrium. Monte Carlo and counterfactual simulations show this structure matters for empirical work. A full-solution estimator that assumes uniqueness can converge to the unstable equilibrium, even when the data were generated by a stable one, while a two-step estimator recovers the correct equilibrium.