The Trustworthiness And Envy-freeness Of The Max-Min Fairness-Based Coalitional And Competitive Mechanism

Research on fair resource allocation or exchange mechanisms has always been a hot topic,be it in communication networks or in social networks.Nodes(agents)in most networks need to maximize their own utility.Therefore,some nodes may cooperate to form different coalitions.The competition between nodes will become competition between the nodes and coalitions or between coalitions and coalitions.That is what we called coalitional game.In the coalitional game,the nodes may cooperate or compete with each other to maximize their own profit.Therefore,different coalitions form.How to design a fair resource allocation mechanism in the coalitional game is a critical problem.A popular resource exchanging mechanism to find a fair resource allocation is called Max-Min Fairness-Based Coalitional(MMFC)Mech-anism[1],which is aimed at finding the max-min resource exchange rate in the resource exchange network.However,whether the MMFC mechanism is trustworthy remains unsolved.What's more,the MMFC mechanism does not consider whether the node's resource allocation are envy-free or not.In this paper,we first demonstrate the trustworthiness of this mechanism,that is,an agent cannot increase its utility by misreporting its resource information.Next,we explores the fairness of MMFC:the allocation derived by MMFC mechanism might seem to be fair.However,the resource allocation derived by the MMFC mechanism might not be envy-free[2].In this paper,we introduce the Envy-Free Max-Min Fairness-Based Coalitional(EFMMFC)Mechanism;Following that,the necessity of the price mechanism in the EFMMFC mechanism and the inevitable existence of the EFMMFC mechanism are proved;at the same time,the key issue in the EFMMFC mechanism-the welfare maximization allocation is explored;Finally,some numerical examples are given to explain the mechanism.