Download this Paper Open PDF in Browser

Between the Prekernel and the Prenucleolus

23 Pages Posted: 22 May 2010  

Ilya V. Katsev

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics

Elena Yanovskaya

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics; National Research University Higher School of Economics

Date Written: April 30, 2010

Abstract

A collection of TU games solutions intermediate between the prekernel and the prenucleolus is considered. Each solution from the collection is parametrized by a positive integer k > 1 and is called the k-prekernel for properties extending those verifying by the prekernel such that the 2-prekernel coincides with the prekernel. If the number of players in a game is less than k, then the k-prekernel of this game coincides with the prenucleolus. All k-prekernels are efficient, covariant, consistent in the sense of Davis-Maschler, and satisfy equal treatment property. K-analogs of balancedness of collections of coalitions and of consistency properties are defined, and with the
help of such properties an axiomatic characterization of the collection of the k-prekernels is given for the class of TU games with an infinite universe set of players.

Keywords: TU-Game, Prekernel, Prenucleolus, Consistency

JEL Classification: C71

Suggested Citation

Katsev, Ilya V. and Yanovskaya, Elena, Between the Prekernel and the Prenucleolus (April 30, 2010). Available at SSRN: https://ssrn.com/abstract=1613244 or http://dx.doi.org/10.2139/ssrn.1613244

Ilya V. Katsev (Contact Author)

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics ( email )

Tchaikovsky st. 1
Saint Petersburg, 191187
Russia

Elena Yanovskaya

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics ( email )

Tchaikovsky st. 1
Saint Petersburg, 191187
Russia

National Research University Higher School of Economics ( email )

Moscow, Moscow 119017
Russia

Paper statistics

Downloads
31
Abstract Views
361