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Cooperative interval games: a survey

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  • R. Branzei
  • O. Branzei
  • S. Alparslan Gök
  • S. Tijs

Abstract

The (re)distribution of collective gains and costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The theory of cooperative interval games provides a new game theoretical angle and suitable tools for answering this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative interval games extends the cooperative game theory literature, and reviews its existing and potential applications in economic and operations research situations with interval data. Copyright Springer-Verlag 2010

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  • 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.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:3:p:397-411
    DOI: 10.1007/s10100-009-0116-0
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    1. Moretti, S. & Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Connection Situations under Uncertainty," Discussion Paper 2008-64, Tilburg University, Center for Economic Research.
    2. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
    3. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    4. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Convex Interval Games," Other publications TiSEM d8704fc2-6edc-46cc-8330-8, Tilburg University, School of Economics and Management.
    5. Judith Timmer & Peter Borm & Stef Tijs, 2005. "Convexity In Stochastic Cooperative Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 25-42.
    6. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    7. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. S. Alparslan-Gök & R. Branzei & V. Fragnelli & S. Tijs, 2013. "Sequencing interval situations and related games," 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. 21(1), pages 225-236, January.
    9. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    10. Moretti, S. & Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Connection Situations under Uncertainty," Other publications TiSEM e9771ffd-ce59-4b8d-a2c8-d, Tilburg University, School of Economics and Management.
    11. Hsiao, Chih-Ru & Raghavan, T E S, 1992. "Monotonicity and Dummy Free Property for Multi-choice Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 301-312.
    12. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    14. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    15. Tijs, S.H., 1990. "Big boss games, clan games and information market games," Other publications TiSEM 87762ef7-823f-451b-b5b3-e, Tilburg University, School of Economics and Management.
    16. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Convex Interval Games," Discussion Paper 2008-37, Tilburg University, Center for Economic Research.
    17. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
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    Cited by:

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    3. 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.
    4. 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.
    5. Deng-Feng Li & Yin-Fang Ye, 2018. "Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method," Operational Research, Springer, vol. 18(1), pages 205-220, April.
    6. ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.
    7. 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.
    8. 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.
    9. 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.
    10. Keyzer, Michiel & van Wesenbeeck, Cornelia, 2011. "Optimal coalition formation and surplus distribution: Two sides of one coin," European Journal of Operational Research, Elsevier, vol. 215(3), pages 604-615, December.
    11. Adil Baykasoğlu & Burcu Kubur Özbel, 2021. "Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty," Operational Research, Springer, vol. 21(3), pages 2149-2179, September.
    12. Troncoso-Valverde, Cristián & Chávez-Bustamante, Felipe, 2024. "Do you want to know a secret? Strategic alliances and competition in product markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1180-1190.
    13. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
    14. Josefa Mula & Marija Bogataj, 2020. "Special issue: engineering digital transformation," 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. 28(1), pages 1-4, March.
    15. 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.
    16. 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).
    17. Chunqiao Tan & Wenrui Feng & Weibin Han, 2020. "On the Banzhaf-like Value for Cooperative Games with Interval Payoffs," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    18. Ankan Bhaumik & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2020. "Hesitant interval-valued intuitionistic fuzzy-linguistic term set approach in Prisoners’ dilemma game theory using TOPSIS: a case study on Human-trafficking," 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. 28(2), pages 797-816, June.
    19. Schumacher, Johannes M., 2021. "Ex-ante estate division under strong Pareto efficiency," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 10-24.
    20. Hsien-Chung Wu, 2018. "Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs," Mathematics, MDPI, vol. 6(11), pages 1-26, November.
    21. 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.
    22. 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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    More about this item

    Keywords

    Cooperative games; Interval data; Interval cores; Convexgames; Big boss games; C71;
    All these keywords.

    JEL classification:

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

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