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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ExampleProblemFormulation<strong>Stability</strong> <strong>and</strong>AccuracyFunctionsLet m = 3, s = 2, J = ({1}, {2, 3}) <strong>and</strong>⎛1 2 1C 0 ⎜= ⎝ 2 1 21 3 2⎞⎟⎠.Assume also that B = (∅, {(0, 0) T , (1, 1) T }), i.e.X = {x 1 , x 2 , x 3 , x 4 }, x 1 = (0, 0, 1) T , x 2 = (0, 1, 0) T ,x 3 = (1, 0, 1) T , <strong>and</strong> x 4 = (1, 1, 0) T .Then C 0 x 1 = (1, 2, 2) T , C 0 x 2 = (2, 1, 3) T , C 0 x 3 = (2, 4, 3) T ,C 0 x 4 = (3, 3, 4) T , <strong>and</strong> JE 3 (C 0 , X) = {x 1 , x 2 }. Us<strong>in</strong>g formula(3), we calculate R 3 (C 0 , J, x 1 ) = 1 2 <strong>and</strong> R3 (C 0 , J, x 2 ) = 1 2 . Ithappens that for both solutions x 1 <strong>and</strong> x 2 , <strong>the</strong> stability radius isequal to 1 2 . To get more <strong>in</strong>formation about x1 <strong>and</strong> x 2 , we maycheck <strong>the</strong> behavior <strong>of</strong> <strong>the</strong>se solutions when <strong>the</strong>y becomenon-equilibria by means <strong>of</strong> calculat<strong>in</strong>g stability functions on<strong>in</strong>terval [0, q(C 0 , X)), q(C 0 , X) = 1 us<strong>in</strong>g formula (1):Sensitivity Analysis <strong>in</strong> Game Theory Yury Nikul<strong>in</strong> - p. 26/29
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