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Allocation in multi-agenda disputes: A set-valued games approach

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  • Lehrer, Ehud
  • Teper, Roee

Abstract

We study allocation problems when agents negotiate across different agendas. Unlike existing papers on multi-agenda disputes, we consider environments in which resources are constrained and investing (time or effort) in one agenda reduces the ability to invest in other agendas. We introduce a class of cooperative games, referred to as set-valued games (SVG): The value of each coalition is a subset of payoff vectors. Each vector is associated with a distribution of the resources that the coalition may allocate across the agendas. In this environment we introduce and analyze the notion of the core. We show that the core allows for more cooperation opportunities and exchanging favors than existing cooperative multi-agenda models. Proving this relies on a general notion of a comparative advantage. It is shown that the classical core characterization, resorting to duality, does not hold in the current setup.

Suggested Citation

  • Lehrer, Ehud & Teper, Roee, 2020. "Allocation in multi-agenda disputes: A set-valued games approach," Games and Economic Behavior, Elsevier, vol. 122(C), pages 440-452.
    • Handle: RePEc:eee:gamebe:v:122:y:2020:i:c:p:440-452
    DOI: 10.1016/j.geb.2020.04.008
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    References listed on IDEAS

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    1. Bloch, Francis & de Clippel, Geoffroy, 2010. "Cores of combined games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2424-2434, November.
    2. Fernandez, F. R. & Hinojosa, M. A. & Puerto, J., 2004. "Set-valued TU-games," European Journal of Operational Research, Elsevier, vol. 159(1), pages 181-195, November.
    3. Hirbod Assa & Sheridon Elliston & Ehud Lehrer, 2016. "Joint games and compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 91-113, January.
    4. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    5. 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.
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    More about this item

    Keywords

    Set-valued games; Core; Balancedness; Logrolling;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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