Analysis of a Cournot Duopoly Model Based on Uncertain Strategy

Abstract

Researches about Cournot model have appeared in previous works, yet all the established models considered only in the certain case, which indicates the players in the game will not change their strategy. Thus, a Cournot duopoly model based on uncertain strategy is designed with payoff matrix. Result shows that complex dynamical properties like bifurcation and chaos in the certain model don’t exist in the uncertain model any more. An index, aggregate profit or A.P., is introduced to demonstrate the performance of the firms in the game process. The indices of the firms are steady in the uncertain model while they are going in the opposite directions in the certain one. Practically, it means simple strategy brings fierce competition while complex strategy leads to mutual benefit. This explains uncertainty of the market can be reduced by rational choices of the firms, a method implemented by firms in the real world unconsciously.