Analysis of Duopoly Output Game With Different Decision-Making Rules

Abstract

The main objective of this paper is to study the effects of output adjustment speed and weight on the dynamics and aggregate profits of a duopoly game model with heterogeneous players. In duopoly game process, one player chooses the bounded rationality strategy and the other adopts the adaptive expectation method. Also the linear inverse demand function and nonlinear cost function are used. The paper analyzes the stability of fixed points, and studies the dynamics of the duopoly model. Then an adaptive controller is constructed to maximize profits by controlling output chaos. Theoretical analysis and numerical simulations show that the duopoly game model has two equilibrium points: one is unstable and the other is locally stable. High output adjustment speed can cause chaotic variation of the outputs, which will decrease the profit of the firm with bounded rationality. The weight variation has little effect on inducing output chaos. The firm with bounded rationality has strong motives to suppress output chaos to maximize its profit. Numerical experiments to verify the effectiveness of the designed controller in this paper. From the profit point of view, the adaptive expectation method is better than the bounded rationality strategy.