Solution Concepts For Cooperative Games Based On The Excess Of Players

Cooperative game theory provides efficient mathematical tool for situations with cooperation,and it can be applied to many other research areas.Players in cooperative games share information and choose strategy to reach a binding agreement,and then form a coalition to obtain maximal payoff.A fair and reasonable allocation rule plays a significant role in promoting the cooperation among players.Many allocation rules are defined based on the excess of players.Generally,excess measures the complaint for players to a given payoff vector.But the classical excess ignores the external effect of the cooperation.Therefore,as to different situations,this thesis extends the concepts of excess and studies the solution concepts based on the defined excess.By investigating different optimization models,we give different characterization of classical solutions and also obtain some new solution concepts.Furthermore,we apply the method to a cost allocation problem and provide efficient theoretical basis for this kind of problem.The main results are as follows:1.Based on the ideal payoff for players,we analyse the formation of the grand coalition and propose new criterion of excess for players.We implement the equal allocation of non-separable costs value as the optimal solution of corresponding optimization models,and also provide different axiomatizations for the equal allocation of non-separable costs value.2.By analysing the formation of the grand coalition,we define a new excess criterion for players.We define the ? equal allocation of non-separable costs value as the unique optimal solution for different optimization models.Furthermore,we characterize the ? equal allocation of non-separable costs value both form the perspective of cooperative and non-cooperative way.3.By introducing the concept of minimal responsibility level,we consider the formation of the players and define the ?-responsibility method for cost sharing problem of cleaning a polluted river.According to the character of the model,we provide axiomatizations of the new method based on no blind cost property and upstream symmetry property respectively.4.We propose the general compromise value for cooperative games based on the maximal and minimal potential payoffs.We reveal the relation between the general compromise value and other classical solution concepts.Furthermore,we provide the axiomatization of the general compromise value.5.We study the solution concepts of the stochastic cooperative games from the perspective of optimization.As to a special type of payoff vectors,we propose the excess for players and construct the corresponding optimization models.By investigating the optimal solutions,we define two solution concepts for stochastic cooperative games: the fairest solution and the most stable solution.