Asynchronous Irrational Behavior Manipulation Conditions In Cooperative Differential Games

Cooperation is the basis of human social activities,cooperative game has become the forefront of international management scientific research.Under dynamic cooperation a player may use ‘irrational' acts to extort additional gains rather than performing a cooperation agreement at the beginning if later circumstances allow.Yeung(2006)present a condition under which even if irrational behaviors appear later in the game the concerned player would still be performing better under the cooperative scheme.Yeung et al(2010)shown that the dynamic Shapley Value computed for the game of emission reduction satisfies the irrational behavior proof condition for coalitions.The study of irrational behavior is the first focus of this paper,and we present a new condition under which even if irrational behaviors appear in the game the concerned player would still be performing better under the cooperative scheme.Furthermore,the later the irrational behaviors appear,i.e.,the more time the player participates in cooperation,the higher payoff the player will get,which can make the cooperation last much longer.For the differential game problem occurred in the infinite interval,we propose a new asynchronous irrational behavior proof(AIBP)condition.Considering the differential game about the problem of control pollution emission among countries,we show that the AIBP condition can make the cooperation last much longer.In addition,for the differential game of the control pollution emission between two neighboring countries,we have obtained the incentive equilibrium strategy and the credibility condition of the model,this is another focus of this paper.We demonstrated that the linear incentive strategy proposed by the control pollution emission game is not always credible.We studied the cost-sharing problem between the two countries and design a mechanism for allocating over time the individual's total cost such that each player instantaneous cost under cooperation is lower than his noncooperative cost at any instant of time.