Strong Stability in Finite Games with Perturbed Payoffs




Nikulin Yury, Emelichev Vladimir

Alexander Strekalovsky, Yury Kochetov, Tatiana Gruzdeva, Andrei Orlov

International Conference on Mathematical Optimization Theory and Operations Research

2021

Communications in Computer and Information Science

Mathematical Optimization Theory and Operations Research: Recent Trends

Communications in Computer and Information Science

1476

372

386

978-3-030-86432-3

978-3-030-86433-0

1865-0929

DOIhttps://doi.org/10.1007/978-3-030-86433-0_26

https://link.springer.com/chapter/10.1007%2F978-3-030-86433-0_26#citeas



We consider a finite game of several players in a normal form with perturbed linear payoffs where perturbations formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. The concept of equilibrium is generalized using the coalitional profile, i.e. by partitioning the players of the game into coalitions. In this situation, two extreme cases of this partitioning correspond to the Pareto optimal outcome and the Nash equilibrium outcome, respectively. We analyze such type of stability, called strong stability, that is under any small admissible perturbations the efficiency of at least one optimal outcome of the game is preserved. The attainable upper and lower bounds of such perturbations are specified. The obtained result generalizes some previously known facts and sheds more light on the combinatorial specific of the problem considered. Some numerical examples illustrating the main result are specified.



Last updated on 2024-26-11 at 19:43