Analysis Of Dynamics Of Multi-team Game With Cooperation And Competition

In multi-team game, based on assumptions that the players cooperate in the same team, the players compete in different teams and the players select the different rational strategies, this paper studies the dynamical system and its complexity of multi-team game under different bounded rationality strategy.Considering these two kinds of objective functions that one is the weighted sum of profits and the other is that the players in the same team can share some of their profits with their team-mates, we propose multi-team Cournot model of weighted sum of profits, multi-team Cournot model of return rate of profit from team-mates and multi-team Bertrand game of return rate of profit from team-mates. Through stability analysis and numerical simulation of each model, we demonstrate that the model parameters have great influence on the stability of the system and on the speed of convergence to the equilibrium point. The researches have shown that selecting the appropriate parameters can not only lead to better cooperation between the players, but also contribute to converge toward equilibrium state of the players in the game soon.We adjust the multi-team Bertrand model dynamically and propose a new discrete dynamical multi-team Bertrand game model by adding feedback control. Through theoretical analysis, combined with parameters which are chaotic in the original system and Schur-Cohn criteria, we obtain the necessary and sufficient conditions for feedback factor when the new system reaching equilibrium. We compare the new system added feedback control with the original by numerical simulation.