Ambiguous games played by players with ambiguity aversion and minimax regret

Xiong, Wei; Luo, Xudong; Ma, Wenjun; Zhang, Minjie

doi:10.1016/j.knosys.2014.06.019

Cited by 7 publications

(8 citation statements)

References 42 publications

(54 reference statements)

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“…Within the process, the ECR based WAC method, shown in Eqs. (30) and (31), is used to combine multiple D numbers, where the weight factors of D numbers are derived from the fuzzy weights of criteria given in Table 3. At the firs step, the fuzzy weights given in Table 3 Now we can fuse the evaluations on all criteria for every strategy.…”

Section: Payoff Matrix Constructionmentioning

confidence: 99%

“…In a perspective of game theory, it constitutes a two-person zero sum or non-constant sum game [40]. Therefore, game theory is feasibly used in researching the adversarial decision making problem [29,30,41]. Based on two aspects of considerations, the representation of human being's uncertain evaluations and methods for decision making, in this paper we suggest a D numbers theory (DNT) based game-theoretic framework for two persons' adversarial decision making under fuzzy environment, where DNT [42,43] is a new uncertainty reasoning theory which generalizes Dempster-Shafer theory [44,45] and already has some applications [46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

Deng

Jiang

2019

International Journal of Approximate Reasoning

111

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Section: Payoff Matrix Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

Deng

Jiang

2019

International Journal of Approximate Reasoning

111

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“…And Bade studies a game‐theoretic framework with the effect of ambiguity aversion on equilibrium outcomes. Moreover, some researchers also discuss the concept of solution to a game with ambiguous payoffs. Although all of these models concern the effect of ambiguity aversion in games, they just focus on part of our payoff types, such as ambiguity lottery or interval payoff.…”

Section: Related Workmentioning

confidence: 99%

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Luo

Jiang

2017

Int. J. Intell. Syst.

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In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.

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“…Existing representative studies are included in [46,47,48], where Dempster–Shafer evidence theory is employed to express ambiguity. In most cases, payoffs are on the basis of linguistic variables or assessments.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the rich studies on interval- or fuzzy-based matrix games, imprecise matrix games with payoffs involving the uncertainty of ambiguity (i.e., discord and non-specificity) have been given less attention. Existing representative studies are included in [ 46 , 47 , 48 ], where Dempster–Shafer evidence theory is employed to express ambiguity. In most cases, payoffs are on the basis of linguistic variables or assessments.…”

Section: Introductionmentioning

confidence: 99%

Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors

Deng

Jiang

Zhang

2017

Sensors

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The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet such a requirement, this paper develops a zero-sum matrix game model with Dempster–Shafer belief structure payoffs, which effectively represents the ambiguity involved in payoffs of a game. Then, a decomposition method is proposed to calculate the value of such a game, which is also expressed with belief structures. Moreover, for the possible computation-intensive issue in the proposed decomposition method, as an alternative solution, a Monte Carlo simulation approach is presented, as well. Finally, the proposed zero-sum matrix games with payoffs of Dempster–Shafer belief structures is illustratively applied to the sensor selection and intrusion detection of sensor networks, which shows its effectiveness and application process.

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Ambiguous games played by players with ambiguity aversion and minimax regret

Cited by 7 publications

References 42 publications

D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors

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