Equilibrium Strategy for Two-Person Zero-Sum Matrix Game with Random Fuzzy Payoffs

Xu, Lin; Li, Jidong

doi:10.1109/apwcs.2010.49

Cited by 2 publications

(1 citation statement)

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“…In another study investigating a two-person zero-sum game with payoffs in the form of fuzzy variables, Xu and Wang (2009) defined the pessimistic and optimistic values of minimax equilibrium strategy in the confidence level of α, modeled it using fuzzy linear programming model and obtained the optimal equilibrium strategy using particle swarm optimization (PSO) algorithm and fuzzy simulation. In another study, Xu and Li (2010) considered payoffs as fuzzy random variables. This means that each payoff is a random variable, the probability density function parameters of which are fuzzy.…”

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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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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Nash Equilibrium in Fuzzy Random Bi-Matrix Games

Achemine,

Larbani

2023

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Most of the existing works on games under uncertainty consider only one type of uncertainty: fuzzy, random, rough, etc. However, in real-world games, it often happens that randomness and fuzziness simultaneously affect the interaction between players and their payoffs. Investigating fuzzy random games is challenging as it is difficult to express the preferences of players in the presence of two different types of uncertainty. This paper presents a new approach to games involving randomness and fuzziness. Specifically, we consider bi-matrix games where the payoffs are fuzzy random variables. Using probability and possibility measures, we formulate related fuzzy chance-constrained games. Then, we introduce Nash equilibrium for these games. Next, we establish sufficient conditions for the existence of this equilibrium. Further, the problem of its computing is formulated as a nonlinear complementarity problem. Finally, examples of market competition games and pollution management are given to illustrate the application potential of the proposed approach. The novelty and advantage of this work are that it grants the players the freedom to choose the probability and possibility confidence/satisfaction levels at which they want Nash equilibrium to be, and equilibrium computation is simpler compared to existing approaches to fuzzy random bi-matrix games.

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Equilibrium Strategy for Two-Person Zero-Sum Matrix Game with Random Fuzzy Payoffs

Cited by 2 publications

References 20 publications

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

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

Nash Equilibrium in Fuzzy Random Bi-Matrix Games

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