Game theoretic Analysis for Cost Allocation of Cooperative Projects of Local Governments

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1) A core index of cooperative games that is defined as minimum of maximal excess of coalitions on condition that sum of payoffs of all players is equal to worth of grand coalition is proposed. A core index which evaluates cooperative games by a real number from excesses of coalitions perspective is useful not only for deciding optimal coalitions structure but also for analyzing market games.2) We analyze cooperative projects of local governments by cooperative game theory. Cooperative game theory has been applied to cost allocation problems in which costs are given for all coalitions. We propose anew formulation in which not only costs but also benefits are given for all coalitions. We show the procedure for deriving a coalition game from a cost allocation problem where benefit exists. Furthermore a concept of optimal coalition structure is introduced and discussed in this model. This new formulation is extended to the case in which externality is allowed.3) Concept of an optimal coalition structure in a game, which plays an important role when applying a cooperative game to a cost allocation problem is introduced. Two methods of determining an optimal coalition structure in a game are proposed. One method is to maximize the sum of total coalition value of sub games; another is to minimize the maximum core indexes of sub games. Properties of both methods are examined. These two methods are applied to the game introduced by a cost allocation problem of local governments which construct jointly water supply facilities.