Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values
研究了合作博弈中边际主义与平等主义的权衡，通过三种方式刻画了夏普利值与平均分配解的凸组合（平等主义夏普利值），包括变玩家集下的一致性、固定玩家集上的单调性以及非合作博弈实施，揭示了二者的根本差异与有趣联系。
One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.