Cournot competition under uncertainty: conservative and optimistic equilibria

In this paper we analyze competition between firms with uncertain demand functions. A duopoly model is considered in which two identical firms producing homogeneous commodities compete in quantities. They face uncertain market demand in a context in which two different future scenarios are possible, and no information about the probability distribution of occurrence of the scenarios is available. This decision-making situation is formalized as a normal-form game with vector-valued utility functions for which the notion of Pareto equilibrium is adopted as a natural extension of that of Cournot equilibrium. Under standard assumptions about the demand functions, we characterize the complete set of Pareto equilibria. In the second part of the paper, we analyse the equilibria to which the agents will arrive depending on their attitude to risk. We find that equilibria always exist if both agents are simultaneously pessimistic or optimistic. In the non-trivial cases, for pessimistic firms, infinitely many equilibria exist, whereas when firms act optimistically, only those pairs of strategies corresponding to the Cournot equilibria in each scenario can be equilibria.