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On large games with bounded essential coalition sizes

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  • Eyal Winter
  • Myrna Wooders

Abstract

We consider games in characteristic function form where the worth of a group of players depends on the numbers of players of each of a finite number of types in the group. The games have bounded essential coalition sizes: all gains to cooperation can be achieved by coalitions bounded in absolute size (although larger coalitions are permitted they cannot realize larger per‐capita gains). We show that the utility function of the corresponding “limit” market, introduced in Wooders (1988, 1994a), is piecewise linear. The piecewise linearity is used to show that for almost all limiting ratios of percentages of player‐types, as the games increase in size (numbers of players), asymptotically the games have cores containing only one payoff, and this payoff is symmetric (treats players of the same type identically). We use this result to show that for almost all limiting ratios of percentages of player‐types, Shapley values of sequences of growing games converge to the unique limiting payoff.

Suggested Citation

  • Eyal Winter & Myrna Wooders, 2008. "On large games with bounded essential coalition sizes," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 191-206, June.
    • Handle: RePEc:bla:ijethy:v:4:y:2008:i:2:p:191-206
    DOI: 10.1111/j.1742-7363.2008.00079.x
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    1. WOODERS, Myrna, 1988. "Large games are market games. 1. Large finite games," LIDAM Discussion Papers CORE 1988042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 131-162, March.
    2. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    3. Sotomayor, Marilda, 2019. "Competition and cooperation in a two-sided matching market with replication," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1030-1056.
    4. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.

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    1. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.

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