Consistency, Monotonicity and Implementation of Egalitarian Shapley Values

One of the main issues in economics 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 tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, we show that all these solutions satisfy the same reduced game consistency. Second, we characterize this class of solutions using monotonicity properties. Finally, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game.