Nash equilibrium strategy for fuzzy non-cooperative games

Li, Cunlin; Zhang, Qiang

doi:10.1016/j.fss.2011.03.015

Cited by 39 publications

(15 citation statements)

References 17 publications

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“…For exogenously givenṼ and̃, an extended bimatrix game with triangular fuzzy payoffs can be transformed into a standard game with triangular fuzzy payoffs by evaluating the utility of each payoff according to (16) and (17). Given an extended bimatrix game G 3 and reference pointsṼ and̃, a transformation…”

Section: Bimatrix Game With Triangular Fuzzy Payoffs and Loss Avementioning

confidence: 99%

“…is defined, where the utility of each payoff for each player is transformed by using the appropriate reference points and loss aversion coefficients according to (16) or (17). For an extended bimatrix game with triangular fuzzy payoffs G 3 , we definẽ…”

Section: Bimatrix Game With Triangular Fuzzy Payoffs and Loss Avementioning

confidence: 99%

“…Campos [9] firstly investigated two-person zero-sum games with fuzzy payoffs. Since then two-person games with fuzzy payoffs, including two-person zero-sum games and bimatrix games, have been investigated by many researchers [10][11][12][13][14][15][16][17][18][19][20][21][22]. Moreover, some credibilistic games are proposed to deal with the games with fuzzy payoffs, including credibilistic strategic game [23][24][25][26] and credibilistic coalitional game [27].…”

Section: Introductionmentioning

confidence: 99%

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Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs

2018

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Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, for 2×2 bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing (increasing) as their own confidence levels when players employ the optimistic (pessimistic) value criterion.

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Section: Bimatrix Game With Triangular Fuzzy Payoffs and Loss Avementioning

confidence: 99%

Section: Bimatrix Game With Triangular Fuzzy Payoffs and Loss Avementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs

2018

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“…Identifying the Nash equilibrium of this problem using certain values of parameters, the dominant minimax equilibrium strategy was achieved. Cunlin and Qiang (2011) developed Maeda's model where payoffs were asymmetric triangular fuzzy numbers. Lui and Kao (2007) developed a method for zerosum games based on the extension principle and α-cuts.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium solution of non-cooperative multiobjective bimatrix game of Z-numbers

Akhbari¹,

Sadi‐Nezhad²

2016

10.5267/j.ijiec

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In this paper we introduce the concept of equilibrium for a non-cooperative multiobjective bimatrix game with payoff matrices and goals of Z-Numbers. In the recent studies of the authors, the problem of finding equilibrium for a non-cooperative bimatrix of Z-Numbers are investigated. Multiple payoffs are often dealt with in games because a decision making problem under conflict usually involves multiple objectives or attributes such as cost, time and productivity. We let each of the objectives of the problem correspond to each of the payoffs of the game. To aggregate multiple goals, we employ two basic methods, one by weighting coefficients and the other by a minimum component. In order to find the equilibrium solution in such circumstances, we developed a mathematical programming problem to maximize the aggregated goal subject to constraint of satisfying an aspiration level of confidence in the equilibrium solution. Finally a method is presented to determine the equilibrium solution with respect to the level of achievement to the aggregated goal.

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“…Fuzzy games in literature are based on the use of classical fuzzy sets (a.k.a Type-1 fuzzy sets) alongside Linear Programming (LP) methods. The most important works have been proposed by Bector and Chandras [3], Campos [4], Delgado, Verdegay and Vila [5], Li [6], Butnariu [7,8], Vijay et al [9], Monroy et al [10], Cunlin and Qiang [11], and Larbani [12]. All those works handle imprecision around the payoffs in the game using Type-1 fuzzy sets/numbers.…”

Section: Introductionmentioning

confidence: 99%

Non-cooperative Games Involving Type-2 Fuzzy Uncertainty: An Approach

Figueroa–García

Medina-Pinzón

Rubio-Espinosa

2014

Computer Information Systems and Industrial Management

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Classical games theory is based on a set of deterministic payoffs that represent different strategies taken by its players. Deterministic (crisp) payoffs are used by homogeneous players while in many social and business scenarios, different uncertainties such as numerical, linguistic, stochastic, etc are involved. This way, we proposed a model for a two-player game problem involving nonprobabilistic uncertainty coming from uncertain fuzzy payoffs, through Interval Type-2 fuzzy numbers. A method for solving this kind of uncertain games is proposed, and an introductory example is shown.

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Nash equilibrium strategy for fuzzy non-cooperative games

Cited by 39 publications

References 17 publications

Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs

Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs

Equilibrium solution of non-cooperative multiobjective bimatrix game of Z-numbers

Non-cooperative Games Involving Type-2 Fuzzy Uncertainty: An Approach

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