A novel uncertain bimatrix game with Hurwicz criterion. (English) Zbl 1436.91003
Summary: In an uncertain bimatrix game, different uncertain equilibrium strategies have been proposed based on different criterions, such as expected value criterion, optimistic value criterion and uncertain measure criterion. This paper further presents an uncertain bimatrix game with Hurwicz criterion and defines a new solution concept Hurwicz Nash equilibrium. Furthermore, its existence theorem is also proved, and a sufficient and necessary condition is presented to find the Hurwicz Nash equilibrium. Finally, an example is provided for illustrating the usefulness of Hurwicz Nash equilibrium.
References:
| [1] | Blau, Ra, Random-payoff two-person zero-sum games, Oper Res, 22, 6, 1243-1251 (1974) · Zbl 0306.90087 |
| [2] | Butnariu, D., Fuzzy games: a description of the concept, Fuzzy Sets Syst, 1, 3, 181-192 (1978) · Zbl 0389.90100 |
| [3] | Campos, L.; Gonzalez, A., Fuzzy matrix games considering the criteria of the players, Kybernetes, 20, 1, 17-28 (1991) · Zbl 0716.90104 |
| [4] | Cassidy, Rg; Field, Ca; Kirby, Mjl, Solution of a satisficing model for random payoff games, Manag Sci, 19, 3, 266-271 (1972) · Zbl 0262.90073 |
| [5] | Charnes, A.; Kirby, Mjl; Raike, W., Zero-zero chance-constrained games, Theory Probab Appl, 13, 4, 628-646 (1968) · Zbl 0206.23201 |
| [6] | Gao, J., Credibilistic game with fuzzy information, J Uncertain Syst, 1, 1, 74-80 (2007) |
| [7] | Gao, J., Uncertain bimatrix game with applications, Fuzzy Optim Decis Mak, 12, 1, 65-78 (2013) · Zbl 1411.91015 |
| [8] | Gao, J.; Yang, X., Credibilistic bimatrix game with asymmetric information and Bayesian optimistic equilibrium strategy, Int J Uncertain Fuzz, 21, supp01, 89-100 (2013) · Zbl 1322.91004 |
| [9] | Gao, J.; Yu, Y., Credibilistic extensive game with fuzzy information, Soft Comput, 17, 4, 557-567 (2013) · Zbl 1264.91019 |
| [10] | Gao, J.; Liu, Zq; Shen, P., On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game, Soft Comput, 13, 2, 127-132 (2009) · Zbl 1156.91305 |
| [11] | Gao, J.; Zhang, Q.; Shen, P., Coalitional game with fuzzy payoffs and credibilistic Shapley value, Iran J Fuzzy Syst, 8, 4, 107-117 (2011) · Zbl 1260.91017 |
| [12] | Gao, J.; Yang, X.; Liu, D., Uncertain Shapley value of coalitional game with application to supply chain alliance, Appl Soft Comput, 56, 551-556 (2017) |
| [13] | Harsanyi, Jc, Games with incomplete information played by ‘Bayesian’ player, part I. The basic model, Manag Sci, 14, 3, 159-182 (1967) · Zbl 0207.51102 |
| [14] | Harsanyi, Jc, Games with incomplete information, Am Econ Rev, 85, 3, 291-303 (1995) |
| [15] | Lio, W.; Liu, B., Residual and confidence interval for uncertain regression model with imprecise observations, J Intell Fuzzy Syst, 35, 2, 2573-2583 (2018) |
| [16] | Liu, B., Uncertainty theory (2007), Berlin: Springer, Berlin · Zbl 1141.28001 |
| [17] | Liu, B., Some research problems in uncertainty theory, J Uncertain Syst, 3, 1, 3-10 (2009) |
| [18] | Liu, B., Uncertainty theory: a branch of mathematics for modeling human uncertainty (2010), Berlin: Springer, Berlin |
| [19] | Liu, Y.; Liu, G., Stable set of uncertain coalitional game with application to electricity suppliers problem, Soft Comput, 22, 17, 5719-5724 (2018) · Zbl 1398.91041 |
| [20] | Maeda, T., Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff, J Math Anal Appl, 251, 2, 885-896 (2000) · Zbl 0974.91004 |
| [21] | Nash, J., Equilibrium points in \(n\)-person games, Proc Natl Acad Sci, 36, 1, 48-49 (1950) · Zbl 0036.01104 |
| [22] | Nishizaki, I.; Sakawa, M., Equilibrium solutions for multiobjective bimatrix games with fuzzy payoffs and fuzzy goals, Fuzzy Sets Syst, 111, 1, 99-116 (2000) · Zbl 0944.91001 |
| [23] | Shen, P.; Gao, J., Coalitional game with fuzzy information and credibilistic core, Soft Comput, 15, 4, 781-786 (2011) · Zbl 1243.91008 |
| [24] | Song, Y.; Fu, Z., Uncertain multivariable regression model, Soft Comput, 22, 17, 5861-5866 (2018) · Zbl 1398.62206 |
| [25] | Wang, Y.; Luo, S.; Gao, J., Uncertain extensive game with application to resource allocation of national security, J Ambient Intell Humaniz Comput, 8, 5, 797-808 (2017) |
| [26] | Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1(Article 17) |
| [27] | Yang, X.; Gao, J., Uncertain core for coalitional game with uncertain payoffs, J Uncertain Syst, 8, 1, 13-21 (2014) |
| [28] | Yang, X.; Gao, J., Linear-quadratic uncertain differential game with application to resource extraction problem, IEEE Trans Fuzzy Syst, 24, 4, 819-826 (2016) |
| [29] | Yang, X.; Gao, J., Bayesian equilibria for uncertain bimatrix game with asymmetric information, J Intell Manuf, 28, 3, 515-525 (2017) |
| [30] | Yang, Xiangfeng; Liu, Baoding, Uncertain time series analysis with imprecise observations, Fuzzy Optimization and Decision Making, 18, 3, 263-278 (2018) · Zbl 1427.62111 |
| [31] | Yao, K.; Liu, B., Uncertain regression analysis: an approach for imprecise observations, Soft Comput, 22, 17, 5579-5582 (2018) · Zbl 1398.62207 |
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