The Nucleolus as a Consistent Power Index in Noncooerative Majority Games

Abstract

This paper studies noncooperative bargaining with random proposers in proper single games. A power index is called consistent if it can be obtained as an equilibrium of the game with random proposers using the index itself as probability vector. Unlike the Shapley-Shubik and Banzhaf indices, the nucleolus has this property. The proof uses the balancedness result in Kohlberg (1971) reinterpreting the balancing wieghts as mixed strategies.noncooperative bargaining;random proposers;nucleolus;consistency;balancedness