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On Simple Outcomes and Cores

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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.

Suggested Citation

  • Marilda Sotomayor, 2016. "On Simple Outcomes and Cores," Working Papers, Department of Economics 2016_05, University of São Paulo (FEA-USP).
    • Handle: RePEc:spa:wpaper:2016wpecon5
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    References listed on IDEAS

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    1. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
    2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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