Existence of Equilibrium Strategies in Fuzzy Stochastic Games with Finite Sets of States and Decisions
Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 623-632

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Noncooperative discounted stochastic $n$-person games are considered; the payoffs at each step are represented by trapezoidal fuzzy numbers. The existence of stationary Nash equilibrium strategies is proved.
Keywords: fuzzy set, stochastic games, equilibrium strategy.
A. S. Shvedov. Existence of Equilibrium Strategies in Fuzzy Stochastic Games with Finite Sets of States and Decisions. Matematičeskie zametki, Tome 107 (2020) no. 4, pp. 623-632. http://geodesic.mathdoc.fr/item/MZM_2020_107_4_a10/
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     title = {Existence of {Equilibrium} {Strategies} in {Fuzzy} {Stochastic} {Games} with {Finite} {Sets} of {States} and {Decisions}},
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[1] J. Nash, “Non-cooperative games”, Ann. of Math. (2), 54 (1951), 286–295 | DOI | MR

[2] L. S. Shapley, “Stochastic games”, Proc. Nat. Acad. Sci. U.S.A., 39 (1953), 1095–1100 | DOI | MR

[3] J.-F. Mertens, S. Sorin, S. Zamir, Repeated Games, CORE Discussion Paper 9420, Univ. Catholique de Louvain, 1994

[4] A. Maitra, W. Sudderth, Discrete Gambling and Stochastic Games, Springer, New York, 1996 | MR

[5] J. Filar, K. Vrieze, Competitive Markov Decision Processes, Springer, New York, 1997 | MR

[6] Y. J. Levy, E. Solan, Stochastic Games, Springer, Berlin, 2017 | DOI

[7] D. Garagic, J. B. Cruz Jr., “An approach to fuzzy noncooperative Nash games”, J. Optim. Theory Appl., 118 (2003), 475–491 | DOI | MR

[8] M. Larbani, “Non cooperative fuzzy games in normal form: a survey”, Fuzzy Sets and Systems, 160 (2009), 3184–3210 | DOI | MR

[9] D.-F. Li, “An effective methodology for solving matrix games with fuzzy payoffs”, IEEE Transactions on Cybernetics, 43 (2013), 610–621 | DOI

[10] A. Chakeri, F. Sheikholeslam, “Fuzzy Nash equilibriums in crisp and fuzzy games”, IEEE Transactions on Fuzzy Systems, 21 (2013), 171–176 | DOI

[11] D. Qiu, Y. Xing, S. Chen, “Solving multi-objective matrix games with fuzzy payoffs through the lower limit of the possibility degree”, Symmetry, 9 (2017), Paper No. 130 | DOI | MR

[12] A. M. Fink, “Equilibrium in a stochastic $n$-person game”, J. Sci. Hiroshima Univ. Ser. A-I Math., 28 (1964), 89–93 | MR

[13] M. Takahashi, “Equilibrium points of stochastic noncooperative n-person games”, J. Sci. Hiroshima Univ. Ser. A-I Math., 28 (1964), 95–99 | MR

[14] G. Bortolan, R. Degani, “A review of some methods for ranking fuzzy subsets”, Fuzzy Sets and Systems, 15 (1985), 1–19 | DOI | MR

[15] R. Yager, “A procedure for ordering fuzzy subsets of the unit interval”, Inform. Sci., 24 (1981), 143–161 | DOI | MR

[16] S. Kakutani, “A generalization of Brouwer's fixed point theorem”, Duke Math. J., 8 (1941), 457–459 | DOI | MR