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Scarcity, competition, and value

Author

Listed:
  • André Casajus

    (HHL Leipzig Graduate School of Management)

  • Harald Wiese

    (Universität Leipzig)

Abstract

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.

Suggested Citation

  • André Casajus & Harald Wiese, 2017. "Scarcity, competition, and value," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 295-310, May.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0536-8
    DOI: 10.1007/s00182-016-0536-8
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Mertens, J F, 1988. "The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages 1-65.
    3. Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167, Elsevier.
    4. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    5. Haimanko, Ori, 2001. "Cost sharing: the nondifferentiable case," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 445-462, June.
    6. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU game; Shapley value; Lovász extension; Strong monotonicity; Partnership; Vector measure game; Mertens value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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