Differentiable comparative statics with payoff functions not differentiable everywhere

In this note we consider Cournot oligopoly. Due to the consideration of several consumers and/ or technologies, the profit function is not differentiable everywhere. We show that Cournot equilibrium never occurs in outputs where profit functions are not-differentiable. This result validates the procedure of differentiating profit functions to perform comparative statics in models where profit functions are not differentiable everywhere.Publicad

Comparative Statics for Market Games: The Strong Concavity Case

In this paper we study the effects of a change in sorne exogenous variable (the number of players or a parameter in the payoff functions) on the strategies played and payoffs obtained in a Nash Equilibrium in the framework of a Market Game (a generalization of the Cournot model)o We assume a strong concavity condition which implies that the best reply function of any player is decreasing on sum of the strategies of the remaining players (Le. strategic substitution). Our results generalize and unify those known in the Cournot model