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Clique games: a family of games with coincidence between the nucleolus and the Shapley value

Author

Listed:
  • Christian Trudeau

    () (Department of Economics, University of Windsor)

  • Juan Vidal-Puga

    () (Research Group of Economic Analysis and Departamento de Estatistica e IO, Universidade de Vigo)

Abstract

We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that players are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two players do not belong to the same clique, there is at most one way to link the two players through a chain of players, with any two adjacent players in the chain belonging to a common clique. We provide multiple examples for clique games, chief among them minimum cost spanning tree problems. This allows us to obtain new correspondence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem.

Suggested Citation

  • Christian Trudeau & Juan Vidal-Puga, 2017. "Clique games: a family of games with coincidence between the nucleolus and the Shapley value," Working Papers 1705, University of Windsor, Department of Economics.
  • Handle: RePEc:wis:wpaper:1705
    as

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    File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1705.pdf
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    References listed on IDEAS

    as
    1. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
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    3. Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
    4. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Discussion Paper 2005-123, Tilburg University, Center for Economic Research.
    5. Subiza, Begoña & Giménez, José Manuel & Peris, Josep E., 2015. "Folk solution for simple minimum cost spanning tree problems," QM&ET Working Papers 15-7, University of Alicante, D. Quantitative Methods and Economic Theory.
    6. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    7. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    8. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    9. repec:eee:matsoc:v:89:y:2017:i:c:p:1-9 is not listed on IDEAS
    10. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
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    12. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
    13. 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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    More about this item

    Keywords

    nucleolus; Shapley value; clique; minimum cost spanning tree.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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