Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations

Yousfi-halimi, Naouel; Radjef, Mohammed Saïd; Slimani, Hachem

doi:10.1007/s10479-017-2570-8

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…Second, artificial intelligence-based approaches are used to solve the multicriteria game. For example, the fuzzy set-based algorithm can calculate PNE solutions by constructing membership functions for fuzzy goals [28,29], and the heuristic algorithm can solve it by using a population evolution strategy [30,31]. However, these algorithms are usually used in problems with low real-time requirements, and their application range is always limited for the problem constraints.…”

Section: Introductionmentioning

confidence: 99%

Multicriteria Game Approach to Air-to-Air Combat Tactical Decisions for Multiple UAVs

Jiang,

Luo,

et al. 2023

J. of Syst. Eng. Electron.

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Air-to-air combat tactical decisions for multiple unmanned aerial vehicles (ACTDMU) are a key decision-making step in beyond visual range combat. Complex influencing factors, strong antagonism and real-time requirements need to be considered in the ACTDMU problem. In this paper, we propose a multicriteria game approach to ACTDMU. This approach consists of a multicriteria game model and a Pareto Nash equilibrium algorithm. In this model, we form the strategy profiles for the integration of air-to-air combat tactics and weapon target assignment strategies by considering the correlation between them, and we design the vector payoff functions based on predominance factors. We propose a algorithm of Pareto Nash equilibrium based on preference relations using threshold constraints (PNE-PRTC), and we prove that the solutions obtained by this algorithm are refinements of Pareto Nash equilibrium solutions. The numerical experiments indicate that PNE-PRTC algorithm is considerably faster than the baseline algorithms and the performance is better. Especially on large-scale instances, the Pareto Nash equilibrium solutions can be calculated by PNE-PRTC algorithm at the second level. The simulation experiments show that the multicriteria game approach is more effective than one-side decision approaches such as multiple-attribute decision-making and randomly chosen decisions.

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Section: Introductionmentioning

confidence: 99%

Multicriteria Game Approach to Air-to-Air Combat Tactical Decisions for Multiple UAVs

Jiang,

Luo,

et al. 2023

J. of Syst. Eng. Electron.

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“…Here p ( V, R ) is the payoff received by a player when player I adopts strategy V , and player II chooses strategy R . Halimi et al (2017) have also proposed a method to refine the Pareto NE in a finite multi-criteria two-person game with pure strategies.…”

Section: Introductionmentioning

confidence: 99%

“…Most available methods can be used to select an NE that fares well over a single criterion like payoff or risk dominance (Halimi et al, 2017; Harsanyi, 1995; Harsanyi & Selten 1988; Schmidt et al, 2003), but there is less work focusing on the selection of NE that focus on both payoff and risk dominance. Also, the existing work concentrates on equilibrium selection from pure NEs or, at best, for games having only one mixed NE.…”

Section: Introductionmentioning

confidence: 99%

A Method to Select Best Among Multi-Nash Equilibria

Punniyamoorthy

Abraham

Thoppan³

2021

Studies in Microeconomics

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A non-zero sum bimatrix game may yield numerous Nash equilibrium solutions while solving the game. The selection of a good Nash equilibrium from among the many options poses a dilemma. In this article, three methods have been proposed to select a good Nash equilibrium. The first approach identifies the most payoff-dominant Nash equilibrium, while the second method selects the most risk-dominant Nash equilibrium. The third method combines risk dominance and payoff dominance by giving due weights to the two criteria. A sensitivity analysis is performed by changing the relative weights of criteria to check its effect on the ranks of the multiple Nash equilibria, infusing more confidence in deciding the best Nash equilibrium. JEL Codes: C7, C72, D81

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