Axiomatizations of the proportional division value
研究了可转移效用博弈中比例分配值的公理化刻画，该值按玩家的独立价值比例分配大联盟的总价值。通过引入比例平衡处理等新公理，给出了该值的多种公理系统。
Abstract We present axiomatic characterizations of the proportional division value for TU-games, which distributes the worth of the grand coalition in proportion to the stand-alone worths of the players. First, a new proportionality principle, called proportional-balanced treatment , is introduced by strengthening Shapley’s symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths. We characterize the family of values satisfying efficiency, weak linearity, and proportional-balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property . Second, we propose appropriate monotonicity axioms, and obtain axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency . Finally, we provide a characterization of proportional standardness.