Consistency And Process Analysis For Allocation Rules For Cooperative Games And Revenue Problems

Cooperative games describe the decision-making situation of cooperation among players in the real world,and mainly study how to distribute the worth of coalition produced by cooperating fairly and reasonably among all players.In order to obtain more payoff,players will revalue their worth to judge the fairness and rationality of allocation rules.An allocation rule satisfies consistency,if it gives the same payoff to players in the original game as it does to players after they revaluing their worth.Consistency has become an important criterion to describe the fairness and rationality of allocation rules.In addition,proper description and characterization of process is conducive to analyzing the advantages and disadvantages of allocation rules and understanding the connotation of allocation rules.This thesis proposes new methods to revalue the worth of coalitions and discusses the associated consistency of values for cooperative games.The distribution process of cooperative game values is described by establishing selfish coefficients.This thesis also constructs a theoretical model of revenue problem and discusses the consistency and process analysis of revenue allocation rules.The main results are as follows:1.We define bilateral associated games for the CIS value(center-of-gravity of imputation set value)and EANS value(equal allocation of non-separable costs value)by considering the possible extra gain and loss of coalitions.We prove that the sequences of repeated bilateral associated games are convergent,then characterize the CIS value and the EANS value with bilateral associated consistency.2.We propose the concept of social selfishness ? ? [0,1],and present the allocation process for the ?-egalitarian Shapley value.Moreover,we build an associated game for all egalitarian Shapley values based on the sum of marginal contributions of all players in a coalition,and characterize the egalitarian Shapley value with associated consistency.3.We put forward the selfish coefficient function and introduce the individual expected rewards of players.By minimizing the deviation between the player's payoff and his individual expected rewards,we define the family of ideal values.On the basis of selfish coefficient function,we provide the properties analysis and process characterization for the family of ideal values.4.We establish the model of revenue problem and define the CP family of revenue sharing rules.Then,we characterize the CP family of revenue sharing rules with bilateral consistency.In addition,we show a series of recursive allocating processes which is coincident with the CP family of revenue sharing rules.Finally,with respect to the revenue sharing rules for the revenue problems,we show a method to normalize these inefficient values for cooperative games,which connects the cooperative games and revenue problems.