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Cooperation under interval uncertainty

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  • S. Alparslan-Gök
  • Silvia Miquel
  • Stef Tijs

Abstract

In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called ψ α -values are introduced and characterizations are given. Copyright Springer-Verlag 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:1:p:99-109
    DOI: 10.1007/s00186-008-0211-3
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    1. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
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    6. 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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    Cited by:

    1. Graziano Pieri & Lucia Pusillo, 2010. "Interval Values for Multicriteria Cooperative Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(2), pages 189-200, June.
    2. O. Palancı & S. Alparslan Gök & G. Weber, 2014. "Cooperative games under bubbly uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 129-137, October.
    3. Rene (J.R.) van den Brink & Osman Palanci & S. Zeynep Alparslan Gok, 2017. "Interval Solutions for Tu-games," Tinbergen Institute Discussion Papers 17-094/II, Tinbergen Institute.
    4. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    5. R. Branzei & S. Gök & O. Branzei, 2011. "Cooperative games under interval uncertainty: on the convexity of the interval undominated cores," 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. 19(4), pages 523-532, December.
    6. Yan-an Hwang & Ming-chuan Chen, 2012. "A new axiomatization of the Shapley value under interval uncertainty," Economics Bulletin, AccessEcon, vol. 32(1), pages 799-810.
    7. 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.
    8. ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.
    9. Sergio Ortobelli Lozza & Tommaso Lando & Filomena Petronio & Tomáš Tichý, 2016. "Asymptotic Multivariate Dominance: A Financial Application," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1097-1115, December.
    10. 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.
    11. Gök Sırma Zeynep Alparslan & Rodica Branzei & Stef Tijs, 2009. "Airport interval games and their Shapley value," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(2), pages 9-18.
    12. Jian Li & Jian-qiang Wang & Jun-hua Hu, 2019. "Interval-valued n-person cooperative games with satisfactory degree constraints," 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. 27(4), pages 1177-1194, December.
    13. Junnosuke Shino & Shinichi Ishihara & Shimpei Yamauchi, 2022. "Shapley Mapping and Its Axiomatizations in n -Person Cooperative Interval Games," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    14. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    15. Alparslan Gök, S.Z. & Branzei, O. & Branzei, R. & Tijs, S., 2011. "Set-valued solution concepts using interval-type payoffs for interval games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 621-626.
    16. Zhang, Qinchunxue & Shu, Lan & Jiang, Bichuan, 2023. "Moran process in evolutionary game dynamics with interval payoffs and its application," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    17. Aymeric Lardon, 2017. "Endogenous interval games in oligopolies and the cores," Annals of Operations Research, Springer, vol. 248(1), pages 345-363, January.
    18. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
    19. Alparslan Gök, S.Z. & Özcan, İ., 2023. "On big boss fuzzy interval games," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1040-1046.
    20. Yu, Xiaohui & He, Mingke & Sun, Hongxia & Zhou, Zhen, 2020. "Uncertain coalition structure game with payoff of belief structure," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    21. Weber, Gerhard-Wilhelm & Defterli, Ozlem & Alparslan Gök, SIrma Zeynep & Kropat, Erik, 2011. "Modeling, inference and optimization of regulatory networks based on time series data," European Journal of Operational Research, Elsevier, vol. 211(1), pages 1-14, May.
    22. Fang-Xuan Hong & Deng-Feng Li, 2017. "Nonlinear programming method for interval-valued n-person cooperative games," Operational Research, Springer, vol. 17(2), pages 479-497, July.
    23. Shinichi Ishihara & Junnosuke Shino, 2023. "Some Properties of Interval Shapley Values: An Axiomatic Analysis," Games, MDPI, vol. 14(3), pages 1-10, June.
    24. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.

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