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A Ramsey bound on stable sets in Jordan pillage games

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  • Manfred Kerber
  • Colin Rowat

Abstract

Jordan [2006] defined ‘pillage games’, a class of cooperative games whose dominance operator is represented by a ‘power function’ satisfying coalitional and resource monotonicity axioms. In this environment, he proved that stable sets must be finite. We use graph theory to reinterpret this result, tightening the bound, highlighting the role played by resource monotonicity, and suggesting a strategy for yet tighter bounds.
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Suggested Citation

  • Manfred Kerber & Colin Rowat, 2011. "A Ramsey bound on stable sets in Jordan pillage games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 461-466, August.
    • Handle: RePEc:spr:jogath:v:40:y:2011:i:3:p:461-466
    DOI: 10.1007/s00182-010-0247-5
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    References listed on IDEAS

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    1. Michael Kremer, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 551-575.
    2. Jordan, J.S., 2006. "Pillage and property," Journal of Economic Theory, Elsevier, vol. 131(1), pages 26-44, November.
    3. Manfred Kerber & Colin Rowat, 2009. "Stable Sets in Three Agent Pillage Games," Discussion Papers 09-07, Department of Economics, University of Birmingham.
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    Cited by:

    1. Manfred Kerber & Colin Rowat & Naoki Yoshihara, 2023. "Asymmetric majority pillage games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1009-1035, December.
    2. Simon MacKenzie & Manfred Kerber & Colin Rowat, 2015. "Pillage games with multiple stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 993-1013, November.
    3. Rowat, Colin & Kerber, Manfred, 2014. "Sufficient conditions for unique stable sets in three agent pillage games," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 69-80.
    4. Beardon, Alan F. & Rowat, Colin, 2013. "Efficient sets are small," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 367-374.
    5. Manfred Kerber & Colin Rowat, 2009. "Stable Sets in Three Agent Pillage Games," Discussion Papers 09-07, Department of Economics, University of Birmingham.

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    More about this item

    Keywords

    Pillage; Cooperative game theory; Stable sets; C71; P14;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • P14 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Property Rights

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