Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
sequential game; risk sensitive; turn selection process; fuzzy numbers; fuzzy utility functions
sequential game; risk sensitive; turn selection process; fuzzy numbers; fuzzy utility functions
Summary:
A particular group of models of sequential games is studied where the order of the turns is not known beforehand by the players, and where the utility functions for each player are fuzzy numbers. For these models, a series of results are proven to show the existence of equilibria under two criteria, and a brief application is described where it usually is not possible to give utilities a precise value, hence, where fuzzy numbers are adequate.
References:
[1] Becerril-Borja, R., Montes-de-Oca, R.: Sequential games with finite horizon and turn selection process: Finite strategy sets case. In: Proc. 5th the International Conference on Operations Research and Enterprise Systems (ICORES 2016) (2016), pp. 44-50. DOI
[2] Becerril-Borja, R., Montes-de-Oca, R.: A family of models for finite sequential games without a predetermined order of turns. In: Operations Research and Enterprise Systems: 5th International Conference ICORES 2016, Rome 2016, Revised Selected Papers, (B. Vitoriano and G. H. Parlier, eds.), pp. 35-51. Springer, Cham 2017. DOI
[3] Becerril-Borja, R., Montes-de-Oca, R.: Incomplete information and risk sensitive analysis of sequential games without a predetermined order of turns. Kybernetika 57 (2021), 312-331. DOI
[4] Borj, O. K., Ramezani, N., Akbarzade, T. M. R.: Using decision trees and a-cuts for solving matrix games with fuzzy payoffs. In: 2014 Iranian Conference on Intelligent Systems 2014, pp. 1-6. DOI
[5] Carrero-Vera, K., Cruz-Suárez, H., Montes-de-Oca, R.: Markov decision processes on finite spaces with fuzzy total rewards. Kybernetika 58 (2022), 180-199. DOI
[6] Cruz-Suárez, H., Montes-de-Oca, R., Ortega-Gutiérrez, R. I.: An extended version of average Markov decision processes on discrete spaces under fuzzy environment. Kybernetika 59 (2023), 160-178. DOI
[7] Fudenberg, D., Tirole, J.: Game Theory. The MIT Press, Boston 1991.
[8] Li, D.-F.: A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers. European J. Oper. Res. 223 (2012), 421-429. DOI
[9] Maschler, M., Solan, E., Zamir, S.: Game Theory. Cambridge University Press, Cambridge 2020. DOI
[10] Nishizaki, I., Sakawa, M.: Fuzzy and Multiobjective Games for Conflict Resolution. Physica-Verlag, Heidelberg, 2001. Zbl 0973.91001
[11] Puri, M. L., Ralescu, D. A.: Fuzzy random variable. J. Math. Anal. Appl. 114 (1986), 409-422. DOI
[12] Rezvani, S., Molani, M.: Representation of trapezoidal fuzzy numbers with shape function. Ann. Fuzzy Math. Inform. 8 (2014), 89-112.
[13] Tadelis, S.: Game Theory: An Introduction. Princeton University Press, Princeton 2013.
[14] Zadeh, L.: Fuzzy sets. Inform. Control 8 (1965), 338-353. DOI | Zbl 0942.00007
Search
Partner of
