On Simple Outcomes and Cores

Marilda Sotomayor ()

No 2016_05, Working Papers, Department of Economics from University of São Paulo (FEA-USP)

Abstract: For a general coalitional game with non-transferable utility (NTU game) and a finite set of players, (N,V), Scarf (1967) proved that every balanced game has a non-empty core. Billera (1970) showed, through an example, that this condition is not always necessary when V(N) has a supremum. By using the concepts of simple outcome and Pareto simple outcome, the present paper provides a weaker condition than balancedness, which is sufficient for the non-emptiness of the core in the general case and is necessary when V(N) has a supremum. It is also necessary for any TU game. Our proof avoids the use of balancedness and specialized mathematical tools. Instead, it is elementary and only employs simple combinatorial arguments.

Keywords: Core; simple payoff vector; Pareto optimal simple outcome (search for similar items in EconPapers)
JEL-codes: C78 D78 (search for similar items in EconPapers)
Date: 2016-03-14
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-upt
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