Stability and Robustness: Reliability in the World of Uncertainty

Payoff functionsProblemFormulationStability andAccuracyFunctionsA vector of payoff functions (payoff profile)p(C, x) := (p 1 (C, x), ..., p m (C, x)) Tconsists of individual payoff functions p i (C, x) for each playeri ∈ N m , which are defined as linear functions on the set ofsolutions X:p i (C, x) := C i x.Here C i is i-th row of matrix C = [c ij ] ∈ R m×m+ ,x := (x 1 , x 2 , ..., x m ) T , x i ∈ X i , i ∈ N m .Note that for each player i ∈ N m , the individual payoff p i (C, x)depends on solution x, i.e. on the strategy chosen by player ias well as the strategies chosen by all the other players. Thusa set of payoff profiles P(C, X) is the followingP(C, X) := {p(C, x) : x ∈ X}.Sensitivity Analysis in Game Theory Yury Nikulin - p. 4/29