On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations

Chandra, Suresh; Aggarwal, Abha

doi:10.1016/j.ejor.2015.05.011

Cited by 36 publications

(27 citation statements)

References 12 publications

(31 reference statements)

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“…Then, in a fuzzy game

italicFG = ((),,, S_{p}, S_{n}, \tilde{A})

, only the payoff matrix is fuzzy, strategy sets for both players are assumed to be crisp. Chandra and Aggarwal's model for TFNs is given below.

((), MOP - normalI) italicMax ((),,, v^{l}, v^{m}, v^{r})

…”

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

“…Chandra and Aggarwal also developed the following model for piecewise fuzzy numbers:

((), VP) 1 italicMax ((),, v_{α_{i}}^{j}, (i = 1, 2, \dots r, j = 1, 2))

…”

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

“…Then problems are solved to find the best value in terms of these α ‐cut levels and their respective strategy mix values. Note that Chandra and Aggarwal's MOP‐I and MOP‐II are special versions of (VP) 1 and (VP) 2 , as optimizing α = 0 and α = 1.…”

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

“…He solved 3 LPs for each component of the triangular fuzzy number (TFN), namely v l , v m , v r (left, middle, and right values of the TFN, respectively) and w l , w m , w r which are defined for players I and II, respectively. However, Chandra and Aggarwal criticized this method because it can yield different mixed strategies for the same player, because it considers the right, middle, and left values of the TFN in separate LPs. Therefore, they suggested a multi‐objective linear programming (MOLP)‐based approach and optimized the components of TFN simultaneously.…”

Section: Introductionmentioning

confidence: 99%

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Solving two‐player zero sum games with fuzzy payoffs when players have different risk attitudes

Koca

Testik

2018

Quality & Reliability Eng

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The aim of this paper is to propose a solution method for 2‐player zero sum games with fuzzy payoffs, which takes different risk attitudes of the players into account. In the proposed model, players' risk attitudes are modeled with α‐cut concept of fuzzy logic, and the game is solved by multi‐objective linear programming approach. The model is implemented on an online marketing problem to show its applicability and use. The game solutions for both players are found by optimizing specific α‐cuts that represent the risk levels of players and given as the game value and corresponding efficient mixed strategies. The results indicated that the proposed model provides a flexible decision‐making environment to the players for their different risk attitudes.

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“…Then, in a fuzzy game

italicFG = ((),,, S_{p}, S_{n}, \tilde{A})

, only the payoff matrix is fuzzy, strategy sets for both players are assumed to be crisp. Chandra and Aggarwal's model for TFNs is given below.

((), MOP - normalI) italicMax ((),,, v^{l}, v^{m}, v^{r})

…”

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

“…Chandra and Aggarwal also developed the following model for piecewise fuzzy numbers:

((), VP) 1 italicMax ((),, v_{α_{i}}^{j}, (i = 1, 2, \dots r, j = 1, 2))

…”

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

Section: Game Theory and Fuzzy Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving two‐player zero sum games with fuzzy payoffs when players have different risk attitudes

Koca

Testik

2018

Quality & Reliability Eng

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“…In the case of Bayesian games, sometimes it is very difficult to characterize the private information of each agent (e.g., ability, level of effort, influence, personality, interest, strategy), to establish the probabilities of the types that each player may assume. In the line of the research of noncooperative fuzzy games, see, e.g., (i) the survey by Larbani,15 (ii) the work by Chandra and Aggarwal, 16 which proposed an algorithm to solve matrix games with payoffs of general piecewise linear fuzzy numbers, (iii) the proposal of Liu and Kao 17 of the application of the extension principle, and (iv) the analyses of the existence of equilibrium solution for a noncooperative game with fuzzy goals and parameters of Kacher and Larbani. Fuzzy set theory, which was introduced by Zadeh, 12 is an excellent basis for studying this type of game in which the payoffs are represented by fuzzy numbers that can be modeled in different ways.…”

Section: Introductionmentioning

confidence: 99%

On Two-Player Interval-Valued Fuzzy Bayesian Games

Asmus

Dimuro

Bedregal

2016

Int. J. Intell. Syst.

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Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval‐based fuzzy Bayesian games, based on interval‐valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not.

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Jagdambika Method for Solving Matrix Games with Fuzzy Payoffs

Verma

Kumar

2018

Recent Developments and the New Direction in Soft-Computing Foundations and Applications

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On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations

Cited by 36 publications

References 12 publications

Solving two‐player zero sum games with fuzzy payoffs when players have different risk attitudes

Solving two‐player zero sum games with fuzzy payoffs when players have different risk attitudes

On Two-Player Interval-Valued Fuzzy Bayesian Games

Jagdambika Method for Solving Matrix Games with Fuzzy Payoffs

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