INSTITUTE OF MATHEMATICAL ECONOMICS

Yan-An Hwang, Peter Sudhölter

Working-Paper No. 297

February 1998

Abstract

We prove that the core on the set of all transferable utility games with players contained in a universe of at least five members can be axiomatized by nonemptiness for two-person flat games, covariance under strategic equivalence, anonymity, individual rationality, the converse reduced game property, the weak reduced game property, and the reduced game property from below (RGPB). Here, a solution satisfies RGPB, if for every member of the solution of the game the following condition is satisfied: Every feasible payoff vector belongs to the solution, whenever its restriction to some coaliton is a member of the solution of the reduced game and its restriction to the complement coalition coincides with the corresponding restriction of the initial vector. Moreover, individual rationality can be replaced by boundedness. Finally we prove that these properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games.

Keywords: TU-game, core, kernel