Oligopoly games with Local Monopolistic Approximation

Abstract

We propose an oligopoly game where quantity setting firms have incomplete information about the demand function. At each time step they solve a profit maximization problem assuming a linear 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 at a Nash equilibrium of the game played under the assumption of full information. 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. In the case of isoelastic demand, we show that the game based on LMA always converges to a Nash equilibrium. This result, compared with “best reply” dynamics, shows that in this particular case less information implies more stability.