The research on price game model and its complex characteristics of triopoly in different decision-making rule

Abstract

Based on a detailed analysis of the international market, we establish a decentralized dynamics model to describe the situation that a new oligarch wishes to enter into a market which has been occupied by two oligarchs, so they have different decision rules. Then we establish and analyze the corresponding continuity system, and in detail discuss the Lyapunov exponent of this system, studying the influence of the parameter’s change to the Lyapunov exponent in three situations. Proceeding to the next step, we make the analysis of the complex dynamics behavior, such as Hopf bifurcation, chaos attractor and initial sensibility. We make a numerical simulation under different conditions, and the result shows that the process of game will tend to a Nash equilibrium at a lower price adjustment speed, and with the increase of the value, the system will appear to be unstable and go into a chaos state gradually. However, for the new entrant, the influence of chaos is not huge, and the new entrant can be seen as a stable element in the chaotic market. The research leads to a good guidance to the market with a new entrant to do the best decision-making.