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Stability kernel in finite games with perturbed payoffs

Emelichev Vladimir, Nikulin Yury

Control and Cybernetics

2022

Vol. 51, No. 1

6--20

The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.

Post-optimal analysis for multicriteria integer linear programming problem with parametric optimality

Emelichev Vladimir, Nikulin Yury

Control and Cybernetics

2020

Vol. 49, No. 2

163--178

This paper addresses a multicriteria problem of integer linear programming with parametric optimality. Parameterizations is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as Pareto and extreme. The parameter space of admissible perturbations in such problem is formed by a set of additive matrices, with arbitrary Hölder’s norms specified in the solution and criterion spaces. The attainable lower and upper bounds for the radii of quasistability are obtained.