TY - JOUR
T1 - Reconciling marginalism with egalitarianism
T2 - consistency, monotonicity, and implementation of egalitarian Shapley values
AU - Ju, Yuan
AU - van den Brink, Rene
AU - Funaki, Yukihiko
N1 - © 2011, the authors. This content is Open Access and made available under a Creative Commons CC-BY-NC Licence.
PY - 2013/3/1
Y1 - 2013/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=83655164168&partnerID=8YFLogxK
U2 - 10.1007/s00355-011-0634-2
DO - 10.1007/s00355-011-0634-2
M3 - Article
VL - 40
SP - 693
EP - 714
JO - Social Choice and Welfare
JF - Social Choice and Welfare
SN - 0176-1714
IS - 3
ER -