Cournot Competition Under Knightian Uncertainty

This article applies a theorem of Nash equilibrium under uncertainty (Dow & Werlang, 1994) to the classic Cournot model of oligopolistic competition. It shows, in particular, how one can map all Cournot-Nash equilibria (which includes the cartel and the null solutions) to only a function of the uncertainty aversion coefficients of the producers. The effects of these parameters on the symmetric equilibrium quantities and output are examined in a comparative statics analysis, under two alternative assumptions: a closed market with an exogenous number of firms and a free-entry/exit regime. In both cases, a collusive effect of the uncertainty aversion on the production is obtained. Under rather few restrictive assumptions, there is a symmetric uncertainty aversion level for the producers at which their optimal quantities and the industry output become equal to the optimal counterpart cartel's outcomes. These results improve upon the literature on collusion since, in contrast to other analogous findings, they enhance that a cooperative cartel may be endogenously generated in a one-shot (noncooperative) game played by uncertainty averse producers. For the competitive case (under free-entry/exit) the paper shows that Cournotian competition among weakely or moderately uncertainty averse producers entails a higher industry output (if the market is large and/or entry is easy) and surely entails lower optimal quantities for the firms than those achieved under uncertainty neutrality. Thus, competition under free-entry/exit in a Knightian uncertainty environment should act to prevent monopoly power for the individual firms.