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A note on potential approach under interval games

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  • Yan-An Hwang
  • Wei-Yuan Yang

Abstract

The main focus of this note is on the interval Shapley value for interval games introduced by Alparslan Gök et al. (Cent. Eur. J. Oper. Res. 18:131–140, 2010 ). In the framework of interval games, we introduce the potential approach and prove that the interval Shapley value can be formulated as the vector of marginal contributions of a potential function. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Yan-An Hwang & Wei-Yuan Yang, 2014. "A note on potential approach under interval games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 571-577, July.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:571-577
    DOI: 10.1007/s11750-012-0271-7
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    References listed on IDEAS

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    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. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    4. 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.
    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Brânzei, R. & Dimitrov, D.A. & Pickl, S. & Tijs, S.H., 2002. "How to Cope with Division Problems under Interval Uncertainty of Claims?," Discussion Paper 2002-96, Tilburg University, Center for Economic Research.
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    Keywords

    Potential; Interval games; 91A12;
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