Dynamic analysis of airline bidding game based on nonlinear cost

Abstract

In this paper, a duopoly airlines bidding game model based on nonlinear variable cost is built, then local and global dynamic characteristics of this bidding game model are extensively researched, with the purpose of discussing the influences of price adjustment speed and of price elasticity coefficient on the evolving regularity of bidding competition of airline. We study the model from both theoretical and numerical simulation aspects. The local and global properties of the model in two-parameter space are analyzed. Moreover, we systematically research the regularity of dynamic evolution about attractors and topological structures of attractors in symmetric and asymmetric information. The simulation results show that there are local steady and multi-steady in this nonlinear model. The adjustment speed and price elasticity coefficient do have significant effects on the model, specifically, once the adjustment speed and price elasticity coefficient exceed the threshold, the game model will irreversibly enter into chaotic state after multiple bifurcations. Furthermore, the speed of price adjustment and the coefficient of price sensitivity have a significant impact on the nonlinear game model. Even subtle changes can cause the system enter bifurcation phenomenon so far as to chaos state. Therefore, the airlines need prudently adjust the parameters of game model in order to keep market competition in steady state in the long run.