<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Stability kernel in finite games with perturbed payoffs

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Stability kernel in finite games with perturbed payoffs"}

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...

Stability kernel in finite games with perturbed payoffs

Published Online: Aug 12, 2022

Page range: 6 - 20

Received: Sep 01, 2021

Accepted: Dec 01, 2021

DOI: https://doi.org/10.2478/candc-2022-0001

Keywords
post-optimal analysis, multiple criteria, kernel stability radius, independent perturbations, finite games, Pareto optimality, Nash equilibrium

© 2022 Vladimir Emelichev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Stability kernel in finite games with perturbed payoffs

Published Online: Aug 12, 2022

Page range: 6 - 20

Received: Sep 01, 2021

Accepted: Dec 01, 2021

DOI: https://doi.org/10.2478/candc-2022-0001

Keywordspost-optimal analysis, multiple criteria, kernel stability radius, independent perturbations, finite games, Pareto optimality, Nash equilibrium

© 2022 Vladimir Emelichev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
post-optimal analysis, multiple criteria, kernel stability radius, independent perturbations, finite games, Pareto optimality, Nash equilibrium