Mathematical Methods of Operations Research

, Volume 56, Issue 3, pp 377–386 | Cite as

Some properties of the core on convex geometries

  • Yoshio Okamoto


A game on a convex geometry was introduced by Bilbao as a model of partial cooperation. We investigate some properties of the core of a game on a convex geometry. First, we show that if a game is quasi-convex, then the core is stable. This result can be seen as an extension of a result by Shapley for traditional cooperative games. Secondly, we show the core on the class of balanced games on a convex geometry has a consistency property, called the reduced game property. Moreover, we axiomatize the core by means of consistency, as is analogous to a result by Peleg for traditional cooperative games.

Key words: Consistency; Convex geometry; Cooperative game; Core; Stability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Yoshio Okamoto
    • 1
  1. 1.Department of Systems Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo, 153-8902, Japan (e-mail:

Personalised recommendations