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A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

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  • Predtetchinski, Arkadi
  • Jean-Jacques Herings, P.

Abstract

It is well--known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general pi-balancedness due to Billera (1970) is a sufficient, but not a necessary condition for the core to be non--empty. This paper gives a natural extension of the pi -balancedness condition that is both necessary and sufficient non--emptiness of the core.
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  • Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
  • Handle: RePEc:eee:jetheo:v:116:y:2004:i:1:p:84-92
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    1. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 427-442.
    2. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395 Elsevier.
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