Oligopoly Games with Local Monopolistic Approximation

In this paper we propose an oligopoly game where quantity setting firms have incomplete information about the (nonlinear) demand function. At each time step they solve a profit maximization problem assuming a linear approximation of the demand function and ignoring the effects of the competitors’ outputs. Despite such a rough approximation, that we call “Local Monopolistic Approximation” (LMA), the repeated game may converge, in the long run, at a Nash equilibrium of the game played under the assumption of full information, thus giving an evolutionary interpretation of the stability of a Nash equilibrium under assumptions. of bounded rationality. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Moreover, in the particular case of isoelastic demand function, we show that the game based on LMA always converges to a Nash equilibrium. This result, compared with “best reply” dynamics obtained under the assumption of compete knowledge of the isoelastic (hence nonlinear) demand , shows that in this case less information implies more stability. The method of LMA approximation proposed in this paper can be extended to Cournot oligopoly games with arbitrary demand functions, as an explicit form of the dynamical system can always be obtained.