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The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set

Author

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  • Lukáš Adam

    (Czech Academy of Sciences)

  • Tomáš Kroupa

    (Università degli Studi di Milano)

Abstract

We introduce the intermediate set as an interpolating solution concept between the core and the Weber set of a coalitional game. The new solution is defined as the limiting superdifferential of the Lovász extension and thus it completes the hierarchy of variational objects used to represent the core (Fréchet superdifferential) and the Weber set (Clarke superdifferential). It is shown that the intermediate set is a non-convex solution containing the Pareto optimal payoff vectors that depend on some chain of coalitions and marginal coalitional contributions with respect to the chain. A detailed comparison between the intermediate set and other set-valued solutions is provided. We compute the exact form of intermediate set for all games and provide its simplified characterization for the simple games and the glove game.

Suggested Citation

  • Lukáš Adam & Tomáš Kroupa, 2017. "The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 891-918, November.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-016-0557-3
    DOI: 10.1007/s00182-016-0557-3
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    References listed on IDEAS

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    1. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, December.
    2. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, June.
    4. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    5. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    6. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    7. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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