Non cooperative fuzzy games in normal form: A survey

Larbani, Moussa

doi:10.1016/j.fss.2009.02.026

Cited by 63 publications

(29 citation statements)

References 45 publications

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“…Also,

δ_{i} (s)

is defined by the minimum operator (i.e., formula ). As pointed out by the work, such an operator is nonsmooth in general and may make the computation of a fuzzy game's Nash equilibrium difficult. However, as shown in formula , we define the final constrained payoff function by a uninorm operator (i.e., formula ), which has no such a problem.…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, their method cannot distinct the material payoff of playing games and the satisfaction degree for the strategies. 30 However, in our method, it is very clear that the concept of satisfaction degree is different from that of material payoff of taking a strategy and they are dealt with by different methods. Also, δ i (s) is defined by the minimum operator (i.e., formula (21)).…”

Section: Related Workmentioning

confidence: 99%

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Games Played under Fuzzy Constraints

Zhang

Luo

Leung

2015

Int. J. Intell. Syst.

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Psychological experiment studies reveal that human interaction behaviors are often not the same as what game theory predicts. One of important reasons is that they did not put relevant constraints into consideration when the players choose their best strategies. However, in real life, games are often played in certain contexts where players are constrained by their capabilities, law, culture, custom, and so on. For example, if someone wants to drive a car, he/she has to have a driving license. Therefore, when a human player of a game chooses a strategy, he/she should consider not only the material payoff or monetary reward from taking his/her best strategy and others' best responses but also how feasible to take the strategy in that context where the game is played. To solve such a game, this paper establishes a model of fuzzily constrained games and introduces a solution concept of constrained equilibrium for the games of this kind. Our model is consistent with psychological experiment results of ultimatum games. We also discuss what will happen if Prisoner's Dilemma and Stag Hunt are played under fuzzy constraints. In general, after putting constraints into account, our model can reflect well the human behaviors of fairness, altruism, self‐interest, and so on, and thus can predict the outcomes of some games more accurate than conventional game theory.

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“…Also,

δ_{i} (s)

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Games Played under Fuzzy Constraints

Zhang

Luo

Leung

2015

Int. J. Intell. Syst.

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“…Another assumption is that data of game is known by players. As Larbani discusses in his paper [21], it is not always possible for players to evaluate outcomes of different strategy profiles for themselves or opposite players. Fuzzy logic and applications may have some advantages to formalize the values of strategies instead of many of the binary logic related dilemmas in crisp game theory.…”

Section: Literature Surveymentioning

confidence: 99%

Fuzzy logic based game theory applications in multi-criteria decision making process

Aplak

Türkbey

2013

Journal of Intelligent &Amp; Fuzzy Systems

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Decision process can be summarized as a process that helps for choosing the optimal alternatives according to suggested objectives by evaluating all environmental effects in problem solving. Nowadays, since environmental effects are more complex, imprecise and multilateral, fuzzy set theory and game theory are widely preferred instruments in decision making process. The aim of this study is to present a hybrid multi-criteria decision making approach which uses artificial intelligence techniques such as fuzzy logic and game theory. This process is considered in two person non-constant sum game theory perspective. The methods in literature about related topics (such as scenario planning and fuzzy TOPSIS) are examined and a hybrid decision making methodology that comprises many decision methods is formed. All phases of this approach are executed in game theory perspective by evaluating mutual strategies of players. In the study, the methodology is explained and a fictitious international disagreement case is used as a numerical example to demonstrate the validity and applicability.

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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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Non cooperative fuzzy games in normal form: A survey

Cited by 63 publications

References 45 publications

Games Played under Fuzzy Constraints

Games Played under Fuzzy Constraints

Fuzzy logic based game theory applications in multi-criteria decision making process

On Two-Player Interval-Valued Fuzzy Bayesian Games

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