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Weighted values and the core in NTU games

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  • Koji Yokote

    (Waseda University)

Abstract

Monderer et al. (Int J Game Theory 21(1):27–39, 1992) proved that the core is included in the set of the weighted Shapley values in TU games. The purpose of this paper is to extend this result to NTU games. We first show that the core is included in the closure of the positively weighted egalitarian solutions introduced by Kalai and Samet (Econometrica 53(2):307–327, 1985). Next, we show that the weighted version of the Shapley NTU value by Shapley (La Decision, aggregation et dynamique des ordres de preference, Editions du Centre National de la Recherche Scientifique, Paris, pp 251–263, 1969) does not always include the core. These results indicate that, in view of the relationship to the core, the egalitarian solution is a more desirable extension of the weighted Shapley value to NTU games. As a byproduct of our approach, we also clarify the relationship between the core and marginal contributions in NTU games. We show that, if the attainable payoff for the grand coalition is represented as a closed-half space, then any element of the core is attainable as the expected value of marginal contributions.

Suggested Citation

  • Koji Yokote, 2017. "Weighted values and the core in NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 631-654, August.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0550-x
    DOI: 10.1007/s00182-016-0550-x
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    References listed on IDEAS

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    1. Bezalel Peleg & Stef Tijs & Peter Borm & Gert-Jan Otten, 1998. "The MC-value for monotonic NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 37-47.
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    4. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    5. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Takuya Masuzawa, 2012. "Strong convexity of NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 699-705, August.
    8. Hinojosa, M.A. & Romero, E. & Zarzuelo, J.M., 2012. "Consistency of the Harsanyi NTU configuration value," Games and Economic Behavior, Elsevier, vol. 76(2), pages 665-677.
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