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Stability and Robustness: Reliability in the World of Uncertainty

Stability and Robustness: Reliability in the World of Uncertainty

Stability and Robustness: Reliability in the World of Uncertainty

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Independent players, no bansProblemFormulation<strong>Stability</strong> <strong>and</strong>AccuracyFunctionsFrom <strong>the</strong>orem 2, we get <strong>the</strong> follow<strong>in</strong>g resultsCorollary 1. For a game with m <strong>in</strong>dependent players <strong>and</strong> no bans(J = ({1}, ..., {m}), B r = ∅ for all r ∈ N m ) <strong>the</strong> stability radius <strong>of</strong> aNash equilibrium x ∗ ∈ NE m (C 0 , X) can be expressed by <strong>the</strong> formulaR S (C 0 , J, x ∗ ) = m<strong>in</strong>i∈N mc 0 ii.In o<strong>the</strong>r words, corollary 1 states that <strong>the</strong> stability radius <strong>of</strong>x ∗ ∈ NE m (C 0 , X) is def<strong>in</strong>ed by elements on <strong>the</strong> pr<strong>in</strong>cipaldiagonal <strong>of</strong> C 0 .Sensitivity Analysis <strong>in</strong> Game Theory Yury Nikul<strong>in</strong> - p. 23/29

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