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An AxiomaticAnalysisofIntervalShapleyValues

Author

Listed:
  • ShinichiIshihara

    (Waseda Institute of Political Economy Waseda University)

  • Junnosuke Shino

    (School of International Liberal Studies, Waseda University)

Abstract

Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty as represented by a closed interval. In this study, we examine two interval game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley like value), and characterize them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young’s strong monotonicity holds on the whole class of interval games.

Suggested Citation

  • ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2214
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    References listed on IDEAS

    as
    1. R. Branzei & O. Branzei & S. Alparslan Gök & S. Tijs, 2010. "Cooperative interval games: a survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 397-411, September.
    2. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
    3. S. Alparslan Gök & R. Branzei & S. Tijs, 2010. "The interval Shapley value: an axiomatization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 131-140, June.
    4. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    5. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 99-109, March.
    6. Fanyong Meng & Xiaohong Chen, 2016. "Cooperative Fuzzy Games with Convex Combination Form," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-25, February.
    7. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    8. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
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    Keywords

    cooperative interval games; interval uncertainty; Shapley value; axiomatization;
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