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.
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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/

[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