An interval-valued cooperative game method with power asymmetry for benefit allocation in marine fishery insurance

Fangxuan Hong; Lixiao Wei; Dengfeng Li; Xi Chen; Fangxuan Hong; Lixiao Wei; Dengfeng Li; Xi Chen

doi:10.3934/era.2026320

Electronic Research Archive

2026, Volume 34, Issue 10: 7420-7447. doi: 10.3934/era.2026320

Previous Article Next Article

Research article

An interval-valued cooperative game method with power asymmetry for benefit allocation in marine fishery insurance

1.
College of Finance, Fujian Jiangxia University, Fuzhou 350108, China
2.
School of Economics and Management, University of Electronic Science and Technology of China, Chengdu 611731, China

Received: 13 July 2026 Revised: 12 August 2026 Accepted: 21 August 2026 Published: 27 August 2026

Cooperative benefit allocation becomes difficult when coalition worths are imprecise and decision rights are asymmetric. This study develops a power-weighted interval-valued core framework that integrates asymmetric voting power with satisfaction-based interval coalition rationality. Individual voting power is derived from coalition criticality in a weighted voting game and aggregated at the coalition level through a least-squares rule, while the resulting max-min allocation model is solved using a bisection procedure based on monotonic feasibility. In a stylized, normalized three-player example motivated by marine fishery insurance, one optimal allocation generated by the proposed model satisfies the adopted efficiency and coalitional rationality conditions, whereas a selected power-adjusted interval Shapley benchmark does not under the same parameterization. Parameter sensitivity analysis further illustrates how voting weights, decision thresholds, and the grand coalition worth interval are associated with changes in power indices and the distribution of allocation uncertainty. The numerical results provide methodological illustrations under a controlled parameterization and demonstrate the feasibility and computational implementation of the proposed solution procedure.
- cooperative game,
- interval-valued core,
- power asymmetry,
- interval ranking,
- marine fishery insurance
Citation: Fangxuan Hong, Lixiao Wei, Dengfeng Li, Xi Chen. An interval-valued cooperative game method with power asymmetry for benefit allocation in marine fishery insurance[J]. Electronic Research Archive, 2026, 34(10): 7420-7447. doi: 10.3934/era.2026320

Related Papers:

Abstract

Cooperative benefit allocation becomes difficult when coalition worths are imprecise and decision rights are asymmetric. This study develops a power-weighted interval-valued core framework that integrates asymmetric voting power with satisfaction-based interval coalition rationality. Individual voting power is derived from coalition criticality in a weighted voting game and aggregated at the coalition level through a least-squares rule, while the resulting max-min allocation model is solved using a bisection procedure based on monotonic feasibility. In a stylized, normalized three-player example motivated by marine fishery insurance, one optimal allocation generated by the proposed model satisfies the adopted efficiency and coalitional rationality conditions, whereas a selected power-adjusted interval Shapley benchmark does not under the same parameterization. Parameter sensitivity analysis further illustrates how voting weights, decision thresholds, and the grand coalition worth interval are associated with changes in power indices and the distribution of allocation uncertainty. The numerical results provide methodological illustrations under a controlled parameterization and demonstrate the feasibility and computational implementation of the proposed solution procedure.

References

[1]	S. Wan, H. Wu, J. Dong, An integrated method for complex heterogeneous multi-attribute group decision-making and application to photovoltaic power station site selection, Expert Syst. Appl., 242 (2024), 122456. https://doi.org/10.1016/j.eswa.2023.122456 doi: 10.1016/j.eswa.2023.122456
[2]	J. Dong, S. Wan, Type-2 interval-valued intuitionistic fuzzy matrix game and application to energy vehicle industry development, Expert Syst. Appl., 249 (2024), 123398. https://doi.org/10.1016/j.eswa.2024.123398 doi: 10.1016/j.eswa.2024.123398
[3]	J. Zhu, G. Tuo, Study on the operation model and its improvement of China Fishery Mutual Insurance Association, Insur. Stud., 5 (2011), 36–46. https://doi.org/10.13497/j.cnki.is.2011.05.001 doi: 10.13497/j.cnki.is.2011.05.001
[4]	K. Borch, Application of game theory to some problems in automobile insurance, ASTIN Bull., 2 (1962), 208–221. https://doi.org/10.1017/S051503610000996X doi: 10.1017/S051503610000996X
[5]	J. Lemaire, An application of game theory: Cost allocation, ASTIN Bull., 14 (1984), 61–81. https://doi.org/10.1017/S0515036100004815 doi: 10.1017/S0515036100004815
[6]	J. Lemaire, Cooperative game theory and its insurance applications, ASTIN Bull., 21 (1991), 17–40. https://doi.org/10.2143/AST.21.1.2005399 doi: 10.2143/AST.21.1.2005399
[7]	R. E. Kihlstrom, A. E. Roth, Risk aversion and the negotiation of insurance contracts, J. Risk Insur., 49 (1982), 372–387. https://doi.org/10.2307/252493 doi: 10.2307/252493
[8]	J. Suijs, P. Borm, A. De Waegenaere, S. Tijs, Cooperative games with stochastic payoffs, Eur. J. Oper. Res., 113 (1999), 193–205. https://doi.org/10.1016/S0377-2217(97)00421-9 doi: 10.1016/S0377-2217(97)00421-9
[9]	J. Linnerooth-Bayer, A. Vári, L. Brouwers, Designing a flood management and insurance system in Hungary: A model-based stakeholder approach, in Integrated Catastrophe Risk Modeling: Supporting Policy Processes, Dordrecht: Springer Netherlands, (2013), 199–216. https://doi.org/10.1007/978-94-007-2226-2_12
[10]	R. J. Aumann, L. S. Shapley, Values of Non-atomic Games, Princeton University Press, (1974), 141–176.
[11]	J. P. Aubin, Coeur et valeur des jeux flous à paiements latéraux, C. R. Acad. Sci. Paris Sér. A., 279 (1974), 891–894.
[12]	İ. Özcan, G. W. Weber, Advances in cooperative game theory under uncertainty: A comprehensive survey, Electron. Res. Arch., 34 (2026), 1342–1362. https://doi.org/10.3934/era.2026061 doi: 10.3934/era.2026061
[13]	J. P. Aubin, Cooperative fuzzy games, Math. Oper. Res., 6 (1981), 1–13. https://doi.org/10.1287/moor.6.1.1 doi: 10.1287/moor.6.1.1
[14]	R. Branzei, D. Dimitrov, S. Tijs, Models in Cooperative Game Theory: Crisp, Fuzzy and Multi-choice Games, Lecture Notes in Economics and Mathematical Systems, Berlin: Springer, (2004), 53–66. https://doi.org/10.1007/3-540-28509-1
[15]	S. Borkotokey, Cooperative games with fuzzy coalitions and fuzzy characteristic functions, Fuzzy Sets Syst., 159 (2008), 138–151. https://doi.org/10.1016/j.fss.2007.07.007 doi: 10.1016/j.fss.2007.07.007
[16]	Y. Azrieli, E. Lehrer, On some families of cooperative fuzzy games, Int. J. Game Theory, 36 (2007), 1–15. https://doi.org/10.1007/s00182-007-0093-2 doi: 10.1007/s00182-007-0093-2
[17]	I. Nishizaki, M. Sakawa, Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters, Fuzzy Sets Syst., 114 (2000), 11–21. https://doi.org/10.1016/S0165-0114(98)00134-1 doi: 10.1016/S0165-0114(98)00134-1
[18]	L. Mallozzi, V. Scalzo, S. Tijs, Fuzzy interval cooperative games, Fuzzy Sets Syst., 165 (2011), 98–105. https://doi.org/10.1016/j.fss.2010.06.005 doi: 10.1016/j.fss.2010.06.005
[19]	Q. Luo, L. Li, Y. She, The fuzzy central core in cooperative games with coalitions' worth represented by fuzzy numbers with respect to Zadeh algebraic orders, Fuzzy Sets Syst., 532 (2026), 109804. https://doi.org/10.1016/j.fss.2026.109804 doi: 10.1016/j.fss.2026.109804
[20]	D. Butnariu, Stability and Shapley value for an n-person fuzzy game, Fuzzy Sets Syst., 4 (1980), 63–72. https://doi.org/10.1016/0165-0114(80)90064-0 doi: 10.1016/0165-0114(80)90064-0
[21]	M. Tsurumi, T. Tanino, M. Inuiguchi, A Shapley function on a class of cooperative fuzzy games, Eur. J. Oper. Res., 129 (2001), 596–618. https://doi.org/10.1016/S0377-2217(99)00471-3 doi: 10.1016/S0377-2217(99)00471-3
[22]	L. Mallozzi, J. Vidal-Puga, An efficient Shapley value for games with fuzzy characteristic function, Fuzzy Optim. Decis. Mak., 24 (2025), 643–668. https://doi.org/10.1007/s10700-025-09461-1 doi: 10.1007/s10700-025-09461-1
[23]	J. Liu, X. Yu, S. Lu, Interval extensions of the Owen value in a cooperative game with a coalition structure and augmenting system, Ann. Oper. Res., 362 (2026), 219–246. https://doi.org/10.1007/s10479-026-07253-3 doi: 10.1007/s10479-026-07253-3
[24]	D. F. Li, Fuzzy Multiobjective Many-Person Decision Makings and Games, National Defense Industry Press, Beijing, (2003), 196–247.
[25]	D. F. Li, Models and Methods for Interval-Valued Cooperative Games in Economic Management, Switzerland, UK: Springer International Publishing, (2016), 45–65. https://doi.org/10.1007/978-3-319-28998-4
[26]	F. X. Hong, D. F. Li, Nonlinear programming method for interval-valued n-person cooperative games, Oper. Res. Int. J., 17 (2017), 479–497. https://doi.org/10.1007/s12351-016-0233-1 doi: 10.1007/s12351-016-0233-1
[27]	S. Zhu, Z. Liu, Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications, AIMS Math., 8 (2023), 29817–29848. https://doi.org/10.3934/math.20231525 doi: 10.3934/math.20231525
[28]	S. Zhu, Z. Liu, G. Ulutagay, M. Deveci, D. Pamučar, Novel α-divergence measures on picture fuzzy sets and interval-valued picture fuzzy sets with diverse applications, Eng. Appl. Artif. Intell., 136 (2024), 109041. https://doi.org/10.1016/j.engappai.2024.109041 doi: 10.1016/j.engappai.2024.109041
[29]	S. Zhu, Y. Li, P. Balaji, A. Thiyagarajan, R. Aluvalu, Z. Liu, An improved interval-valued picture fuzzy TOPSIS approach based on new divergence measures for risk assessment, Comput. Model. Eng. Sci., 144 (2025), 2099–2121. https://doi.org/10.32604/cmes.2025.068734 doi: 10.32604/cmes.2025.068734
[30]	Z. Yu, D. Wang, A. M. Kassim, S. Zhu, Z. Liu, An extended interval-valued Pythagorean fuzzy VIKOR approach with logarithmic distance measures for service quality evaluation of university library, J. Math., 2025 (2025), 9966857. https://doi.org/10.1155/jom/9966857 doi: 10.1155/jom/9966857
[31]	S. Wan, X. Chen, J. Dong, Y. Gao, Probabilistic linguistic group bi-matrix game and applications, Eng. Appl. Artif. Intell., 164 (2026), 113221. https://doi.org/10.1016/j.engappai.2025.113221 doi: 10.1016/j.engappai.2025.113221
[32]	L. S. Shapley, M. Shubik, A method for evaluating the distribution of power in a committee system, Am. Polit. Sci. Rev., 48 (1954), 787–792. https://doi.org/10.2307/1951053 doi: 10.2307/1951053
[33]	J. F. Banzhaf, Ⅲ, Weighted voting doesn't work: A mathematical analysis, Rutgers Law Rev., 19 (1965), 317–343.
[34]	R. Gardner, Value of voting games, in 5th IFAC/IFORS Conference on Dynamic Modelling and Control of National Economies, (1987), 405–407. https://doi.org/10.1016/B978-0-08-034795-0.50073-5
[35]	R. Moore, Methods and Applications of Interval Analysis, Society for Industrial and Applied Mathematics, (1979), 9–17. https://doi.org/10.1137/1.9781611970906
[36]	H. Ishibuchi, M. Tanaka, Multiobjective programming in optimization of the interval objective function, Eur. J. Oper. Res., 48 (1990), 219–225. https://doi.org/10.1016/0377-2217(90)90375-L doi: 10.1016/0377-2217(90)90375-L
[37]	C. Y. Hu, R. B. Kearfott, A. D. Korvin, V. Kreinovich, Knowledge Processing with Interval and Soft Computing, London: Springer Verlag, (2008), 1–12. https://doi.org/10.1007/978-1-84800-326-2
[38]	S. Z. Alparslan Gök, O. Branzei, R. Branzei, S. Tijs, Set-valued solution concepts using interval-type payoffs for interval games, J. Math. Econ., 47 (2011), 621–626. https://doi.org/10.1016/j.jmateco.2011.08.008 doi: 10.1016/j.jmateco.2011.08.008
[39]	K. Sikorski, Bisection is optimal, Numer. Math., 40 (1982), 111–117. https://doi.org/10.1007/BF01459080 doi: 10.1007/BF01459080
[40]	X. Yu, Q. Zhang, Profit allocation in production cooperative game based on interval Shapley value, Trans. Beijing Inst. Tech., 28 (2008), 656–659. https://doi.org/10.15918/j.tbit1001-0645.2008.07.002 doi: 10.15918/j.tbit1001-0645.2008.07.002
[41]	L. Gronbaek, M. Lindroos, G. Munro, P. Pintassilgo, B. Turris, The avoidance of unwanted catch and cooperation: The case of the British Columbia groundfish trawl fishery, ICES J. Mar. Sci., 80 (2023), 483–491. https://doi.org/10.1093/icesjms/fsac005 doi: 10.1093/icesjms/fsac005
[42]	G. Owen, Values of games with a priori unions, in Mathematical economics and game theory: Essays in honor of Oskar Morgenstern, Berlin, Heidelberg: Springer Berlin Heidelberg, (1977), 76–88. https://doi.org/10.1007/978-3-642-45494-3_7
[43]	D. Schmeidler, The nucleolus of a characteristic function game, SIAM J. Appl. Math., 17 (1969), 1163–1170. https://doi.org/10.1137/0117107 doi: 10.1137/0117107
[44]	S. Z. Alparslan Gök, R. Branzei, S. Tijs, The interval Shapley value: An axiomatization, Cent. Eur. J. Oper. Res., 18 (2010), 131–140. https://doi.org/10.1007/s10100-009-0096-0 doi: 10.1007/s10100-009-0096-0
[45]	İ. Özcan, S. Z. Alparslan Gök, G. W. Weber, Peer group situations and games with fuzzy uncertainty, J. Ind. Manage. Optim., 20(2024), 428–438. https://doi.org/10.3934/jimo.2023084 doi: 10.3934/jimo.2023084
[46]	J. H. Friedman, Multivariate adaptive regression splines, Ann. Statist., 19 (1991), 1–67. https://doi.org/10.1214/aos/1176347963 doi: 10.1214/aos/1176347963
[47]	M. Müller, Estimation and testing in generalized partial linear models—A comparative study, Stat. Comput., 11 (2001), 299–309. https://doi.org/10.1023/A:1011981314532 doi: 10.1023/A:1011981314532
[48]	L. S. Shapley, Stochastic games, Proc. Natl. Acad. Sci. USA, 39 (1953), 1095–1100. https://doi.org/10.1073/pnas.39.10.1095 doi: 10.1073/pnas.39.10.1095
[49]	A. Ben-Tal, A. Nemirovski, Robust convex optimization, Math. Oper. Res., 23 (1998), 769–805. https://doi.org/10.1287/moor.23.4.769 doi: 10.1287/moor.23.4.769
[50]	I. Baltas, A. Xepapadeas, A. N. Yannacopoulos, Robust control of parabolic stochastic partial differential equations under model uncertainty, Eur. J. Control, 46 (2019), 1–13. https://doi.org/10.1016/j.ejcon.2018.04.004 doi: 10.1016/j.ejcon.2018.04.004

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)