Research And Application Of Solving Cooperative Game Under Uncertain Payoffs

In traditional solution of cooperative game,it is usually assumed that the payoffs of coalitions are determined or the interval or probability distribution of the value of the coalitions payoffs by the players can form common knowledge.In reality,the payoffs of coalitions are often uncertain.There are differences in individual experience and information,individual rationality,situational judgment,and interest appeal among players.It is often difficult to reach a consensus on the value of coalitions payoffs,especially in the case of asymmetric information and uncertain information.Under the condition that the players have different opinions on the uncertain value of the coalitions payoffs,the formation of the coalition allocation scheme is usually the result of multiple rounds of negotiations among the players based on individual rationality and judgment,and during the negotiation process,they influence and compromise each other.Finally,the proposed allocation scheme gradually converge.At first,this article describes the payoffs of the players under the uncertain payoffs of the coalitions,sets the validity conditions of the allocation,and makes a new characterization of cooperative games.Then,the multi-objective particle swarm optimization(MPSO)is improved to solve the cooperative game problem,the dispersion function and the strategy function are proposed,and the the improved multi-objective particle swarm optimization model is established.Finally,the resolving thoughts and modeling ideas of the multi-objective particle swarm algorithm are used to simulate the negotiation behavior in reality.The stigmergy of the swarm intelligence and negotiating strategy model of cooperative game are designed to solve the cooperative game under the uncertainty of coalitions payoffs.At the mean time,the relevant properties of the negotiating strategy solution of cooperative game are proved.Through data simulation and example analysis,it can be known that:(1)The allocation scheme of cooperative game is the result of the players through communication and negotiation.The initial distribution scheme proposed by the players,the outcome of the negotiation will be affected by the initial and termination values of the learning factors,etc.(2)During the negotiation process,the adjustment of the allocation schemes proposed by the players and the dispersion of the schemes will decrease gradually,then the final schemes tend to be consistent.(3)In the allocation scheme calculated at last,there is an inverse relationship between the certain payoffs and the uncertain payoffs,which reflects the coexistence relationship between the income and the risk in reality.It can effectively achieve the distribution of benefits and the sharing of risks,as well as reflect the individual differences among the players.This paper provides a new idea and method for solving cooperative game when the payoffs of coalitions are uncertain,and provides an "guidance" for solving the cooperative game problem in reality.