Poisson–Cournot games

We construct a Cournot model with uncertainty in the number of firms in the industry. We model such an uncertainty as a Poisson game and characterize the set of equilibria after deriving novel properties of the Poisson distribution. When marginal costs are zero, the number of equilibria increases with the expected number of firms (n) and for n >= 3 every equilibrium exhibits overproduction relative to the model with deterministic population size. For a fixed n, overproduction is robust to sufficiently small marginal costs. The set of equilibria can be Pareto ranked. If n >= 3, even the expected consumer surplus induced by the lowest quantity equilibrium is larger than the consumer surplus in the model without population uncertainty.