Quantity Competition under Asymmetric Information without Common Priors: An Indirect Evolutionary Approach

The common prior assumption asserts that the beliefs of agents in different states of the world are their posteriors based on a common prior and possibly some private signal. Common priors are pervasive in most economic models of incomplete information, oligopoly models with asymmetrically informed firms being no exception. We dispose of the common prior assumption in a Cournot oligopoly with uncertain costs and allow firms to entertain arbitrary priors about the other firms' cost-types. Only Nature is aware of the true probability distribution of the costs and determines via the true distribution which priors will be evolutionarily stable. To check whether the evolutionarily stable priors satisfy the commonness requirement we present two alternative models. In the first model, firms believe that all other firms entertain the same beliefs about the distribution of marginal costs and Nature's priors are not the only evolutionarily stable priors. In a second model with the possibility of asymmetric priors Nature's priors are not evolutionarily stable.