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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.

Keywords: game theory, robust Nash point, robust correlated equilibrium, robustness analysis, payoff uncertainty

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