Mean Field Games Model With Application To Coal Enterprise Of Sea Ports

The mean-field games is a mathematical tool in the competitive environment for enterprises how to make decisions. If the companies are the participants of games, the mean field theory can focus on the influence of the complex environment that each participant facing, with the average effect replace the single effect, so enterprises will make better decisions for avoiding risks, and bring more expected benefit for these enterprises.First, mean-field games model is established to study the system of asymptotic behavior. In the model the number of participants is N, in which each individual interacts with other randomly selected players, the action and the state of each participant together determines the instantaneous payoff for all participants. They also determines the transition probability of participants get to the next state. Participants’ goal is to maximize expected return. Under indistinguishability assumptions, the average field will converge to a certainty measure, the measure meet a nonlinear ordinary differential equation in any smoothly strategy, and the process of each player’s interaction in average-field is equivalent to the process of Markov decision evolutionary games.Second, the mean-field differential game model is established according to the risk sensitivity of under regularity assumptions. After analysis the standard risk sensitivity of differential game theory, we know that the mean-field value of cost function(with the exponentiated form) coicides with the value function of a H-J-B equation(with quadratic term). The equivalent mean-field risk-neutral problem is formulated to shows that the mean-field equilibria are the solution of the H-J-B equation, PFK equation and the MC-V equation that study the individual state under the limit conditions.Finally, in this paper taking coal enterprises of Qinhuangdao port as the object, we analyzed the theoretical research results of this paper. Under the guidance of the mean-field theory, we know that the coal enterprises of port how to make more effective strategies and how to avoid risk and maximize corporate profits by numerical results in the game.