Stability and Robustness: Reliability in the World of Uncertainty

Relative errorProblemFormulationStability andAccuracyFunctionsNamely, in case of J-equilibrium we introduce forx ∗ ∈ JE(C 0 , X) and a given matrix C ∈ R m×m+ the relativeerror of this solution:ε(C, J, x ∗ ) := maxr∈N smax minx∈W J r (x∗ )p i (C, x ∗ ) − p i (C, x).i∈J r p i (C, x)Observe that for an arbitrary C ∈ R m×m+ we haveε(C, J, x ∗ ) ≥ 0. If ε(C, J, x ∗ ) > 0, then x ∗ ∉ JE(C, X) and thispositive value of the relative error may be treated as a measureof inefficiency of the strategy profile x ∗ for the game with matrixC.The equality ε(C, J, x ∗ ) = 0 formulates in general onlynecessary condition for x ∗ to be J-equilibrium, i.e.ε(C, J, x ∗ ) = 0 does not guarantee that x ∗ ∈ JE m (C, X).Sensitivity Analysis in Game Theory Yury Nikulin - p. 10/29