A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game
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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- 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.
- Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998.
"Cooperative games in permutational structure,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 427-442.
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