New Analyses of Duopoly Game with Output Lower Limiters

Abstract

In the real business world, player sometimes would offer a limiter to their output due to capacity constraints, financial constraints, or cautious response to uncertainty in the world. In this paper, we modify a duopoly game with bounded rationality by imposing lower limiters on output. Within our model, we analyze how lower limiters have an effect on dynamics of output and give proof in theory why adding lower limiters can suppress chaos. We also explore the numbers of the equilibrium points and the distribution of conditioned equilibrium points. Stable region of the conditioned equilibrium is discussed. Numerical experiments show that the output evolution system having lower limiters becomes more robust than without them, and chaos disappears if the lower limiters are big enough. The local or global stability of the conditional equilibrium points provides a theoretical basis for the limiter control method of chaos in economic systems.