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Graph-restricted games and their inheritance of properties

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  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Vermeulen, Dries

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory, RS: GSBE MCM)

Abstract

For communication situations where the communication possibilities of players are modeled by an undirected graph, we study to what extent Myerson’s graph-restricted game inherits properties from the original transferable utility game. We focus on monotonicity, additivity, superadditivity, convexity, imputation admissibility, balancedness, total balancedness, population monotonic allocation schemes, and exactness. For each of these properties, we characterize all communication graphs that guarantee the inheritance. We present existing results from the literature and we provide new results.

Suggested Citation

  • Dietzenbacher, Bas & Vermeulen, Dries, 2025. "Graph-restricted games and their inheritance of properties," Research Memorandum 003, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2025003
    DOI: 10.26481/umagsb.2025003
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    References listed on IDEAS

    as
    1. J. Schouten & B. Dietzenbacher & P. Borm, 2022. "The nucleolus and inheritance of properties in communication situations," Annals of Operations Research, Springer, vol. 318(2), pages 1117-1135, November.
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    6. van den Nouweland, Anne & Borm, Peter, 1991. "On the Convexity of Communication Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 421-430.
    7. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    8. Marco Slikker, 2000. "Inheritance of properties in communication situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 241-268.
    9. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    10. Driessen, T.S.H. & Tijs, S.H., 1985. "The t-value, the core and semiconvex games," Other publications TiSEM 016b6b5d-a476-44ca-bd05-7, Tilburg University, School of Economics and Management.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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