Some properties of the core on convex geometries

Yoshio Okamoto

Mathematical Methods of Operations Research, 2003, vol. 56, issue 3, 377-386

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2003

Keywords: Key words: Consistency; Convex geometry; Cooperative game; Core; Stability, (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s001860200218

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