Equity analysis of public investments : pure and mixed game-theoretic solutions

Abstract

Contemporary cost-benefit and cost-effectiveness analysis of public investments often deal with complex situations. There may be not one purpose or objective but many as well as more than one decision-maker. In such cases there exists an efficiency and an equity problem to be solved. The efficiency problem deals with the optimal capacity of the public investment, given all purposes. The equity problem deals with the question of how to allocate costs among different purposes or objectives (cost allocation problem) and/or among the various decision-makers (cost sharing problem) . In section 2.a brief review will be given of some important traditional and contemporary procedures which deal with cost allocation or cost sharing problems in a game-theoretic framework. These methods do not always seem satisfactory. Thus, in section 3. a new solution corncept is proposed : the weighted value of an n-person coopterative game. But the weighted value may be in contradiction to the core of the game. Then mixed solutions are suggested which reconcile both pure solution concepts (section 4.). In section 4.1. it is supposed that the core exists. Then either the weighted value belongs to the core or it does not. In the second case a tax-subsidy scheme may be devised such that the weighted value is modified to be in the core (section 4.1.2.), or the core is modified such that the weighted value is an element of this modified core (section 4.1.3.). If the core does not exist the weighted value is the solution (section 4.2.1.). However, one may calculate the fictitious strong e-core and thus calculate conditional mixed solutions (section 4.2.2.).