Abstract
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 \(n\ge 3\) 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 \(n\ge 3\), even the expected consumer surplus induced by the lowest quantity equilibrium is larger than the consumer surplus in the model without population uncertainty.
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We thank the Editor and anonymous referees for their useful suggestions. We also thank Rabah Amir, Leo Ferraris, Arghya Ghosh, Hongyi Li, Shengyu Li, Diego Lubian and Diego Moreno for helpful comments. Francesco and Claudia thank financial support from the Italian Ministry of Education, PRIN 2017, grant number 2017K8ANN4. Carlos thanks research support from the Australian Research Council’s Discovery Project DP190102629. The usual disclaimer applies.
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De Sinopoli, F., Künstler, C., Meroni, C. et al. Poisson–Cournot games. Econ Theory 75, 803–840 (2023). https://doi.org/10.1007/s00199-022-01425-5
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DOI: https://doi.org/10.1007/s00199-022-01425-5