A NOVEL APPROACH TO ROBUSTNESS ANALYSIS FOR THE SOLUTIONS OF THE GAMES WITH APPROXIMATE PAYOFFS

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VEISI GELAREH; ASGHARIAN RAJAB

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Journal: Journal of Control Year:2012 | Volume:6 | Issue:2 Page(s): 65-76

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Title

A NOVEL APPROACH TO ROBUSTNESS ANALYSIS FOR THE SOLUTIONS OF THE GAMES WITH APPROXIMATE PAYOFFS

Author(s)

VEISI GELAREH | ASGHARIAN RAJAB | Issue Writer Certificate

Keywords

GAME THEORYQ3

ROBUST NASH POINTQ3

ROBUST CORRELATED EQUILIBRIUMQ3

ROBUSTNESS ANALYSISQ3

PAYOFF UNCERTAINTYQ3

Abstract

When using GAME THEORY for modeling real- world problems, players’ payoffs are usually known approximately. Literature reveals that some authors have modeled the approximate payoffs using stochastic or fuzzy variables and some others have used robust optimization techniques to solve these games. Surprisingly little work has been done on ROBUSTNESS ANALYSIS of real- world’s games solutions.In this paper, we propose two simple and practical measures to assess robustness degrees of Nash equilibria. These measures quantitatively show how Nash points behave in the presence of uncertainty and they can be used as refinements of Nash equilibrium. Also we propose two novel approaches to assess robustness degrees of correlated equilibria. One approach is a quantitative way to calculate robustness degrees and the other is a comparative measure to rank correlated equilibria in order of their robustness. We suggest that the decision maker may be able to find more robust solutions in the set of non- Nash correlated equilibria. Moreover, we present a method to improve robustness of Nash points. The improvement algorithm searches for more robust solutions in a neighborhood around a Nash point.We validate our methods with some numerical examples. The examples verify the efficiency of the methods.

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APA: Copy

VEISI, GELAREH, & ASGHARIAN, RAJAB. (2012). A NOVEL APPROACH TO ROBUSTNESS ANALYSIS FOR THE SOLUTIONS OF THE GAMES WITH APPROXIMATE PAYOFFS. JOURNAL OF CONTROL, 6(2), 65-76. SID. https://sid.ir/paper/120864/en

Vancouver: Copy

VEISI GELAREH, ASGHARIAN RAJAB. A NOVEL APPROACH TO ROBUSTNESS ANALYSIS FOR THE SOLUTIONS OF THE GAMES WITH APPROXIMATE PAYOFFS. JOURNAL OF CONTROL[Internet]. 2012;6(2):65-76. Available from: https://sid.ir/paper/120864/en

IEEE: Copy

GELAREH VEISI, and RAJAB ASGHARIAN, “A NOVEL APPROACH TO ROBUSTNESS ANALYSIS FOR THE SOLUTIONS OF THE GAMES WITH APPROXIMATE PAYOFFS,” JOURNAL OF CONTROL, vol. 6, no. 2, pp. 65–76, 2012, [Online]. Available: https://sid.ir/paper/120864/en

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