Stability Analysis For A Cooperative Game Model

On the basis of Cournot model with bounded rationality, we improve the model. We build a cooperative Cournot model with bounded rationality, a three-oligopolist model and a two-team Cournot game. Through the analysis on the model and numerical simulation with the Matlab, we try to supply the theoretic reference for making the strategy of the firm and the development of the firm. The main content is depicted as follows:1. Make a comprehensive introduction of the stability theory and the research of economic chaos and the Cournot model. Make a comprehensive introduction of the multi-team competitive system, especially multi-team Cournot game.2. "Cooperative competition" has become a new competitive mode under the economic globalization. Under this context, the firm needs to seek associates in order to exist and develop in the furious market competition. So there are several cooperative firms competing and several-team firms competing in the market.3. We build a cooperative Cournot model with bounded rationality. Analyzing the stability of the equilibrium points and pointing out the stable range of Nash equilibrium point and its influencing factors. Through selecting the rate of profit assignment between two firms, we compare the equilibrium profit and output of cooperative firms with that of non-cooperative firms and we also compare the stable range of Nash equilibrium point of cooperative firms with that of non-cooperative firms.4. A three-oligopolist discrete dynamical model with bounded rationality is set up. We study the influence of the equilibrium output and profit of the two cooperative firms on the third one. It indicates that because of the cooperation of two firms the third one must enhance its output in order to get more profit. The third one needs more cost because of the enhancement of the output. As the third firm sees the cooperative firms plunge less output but they get more profit , it should seek copartners to strengthen its competitive dominance.5. We study a dynamical two-team Cournot game with nonlinear cost and analyze the stability of inner equilibrium point of it. Through numerical, we compare the equilibrium output and profit of two-team Cournot game with those of their competition as oligopolies and find that the profit of each firm in the same team is higher than the profit of their competition as oligopolies but the output is lower. This indicates that the firms in same team can reach Pareto Optimality if they adjust assignment of the profit properly.