The Procedural Surplus Values for Cooperative Games

In this paper, we introduce a new class of values for cooperative games, named procedural surplus values, which is determined by procedures of sharing marginal surplus. Considering that the level of solidarity among players in a coalition may be related to the size of the coalition, this class of values combines marginalistic and egalitarian principles on the basis of the coalition size. Then we provide two axiomatizations for the whole class of procedural surplus values and each value in this class, respectively. We also discuss the relationships between this class of values and three other classes of values, including the least square family, the generalized consensus values and the procedural values. Interestingly, the Shapley value is the unique intersection of the classes of procedural surplus values and procedural values. Finally, we provide a non-cooperative interpretation of any given procedural surplus value by a bidding mechanism