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. R. van den Brink (B)
To generalize the standard solution for 2-person TU games into n-person cases, this paper introduces a recursive two-sided negotiation process to establish cooperation between all players. This leads to a new solution concept for cooperative games: the consensus value. An explicit comparison with the Shapley value is provided, also at the axiomatic level. Moreover, a class of possible generalizations of the consensus value is introduced and axiomatized with the Shapley value at one end and the equal surplus solution at the other. Finally, we discuss a non-cooperative mechanism which implements the consensus value.
This paper provides a framework for implementing and comparing several solution concepts for transferable utility cooperative games. We construct bidding mechanisms where players bid for the role of the proposer. The mechanisms differ in the power awarded to the proposer. The Shapley, consensus and equal surplus values are implemented in subgame perfect equilibrium outcomes as power shifts away from the proposer to the rest of the players. Moreover, an alternative informational structure where these solution concepts can be implemented without imposing any conditions of the transferable utility game is discussed as well.JEL classification codes: C71; C72; D62.
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