https://doi.org/10.1140/epjb/s10051-021-00112-z
Regular Article - Statistical and Nonlinear Physics
General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games
Institute for Technical Physics and Material Sciences, Centre for Energy Research, P. O. Box 49, 1525, Budapest, Hungary
Received:
27
April
2021
Accepted:
2
May
2021
Published online:
17
May
2021
Two-person games are used in many multi-agent mathematical models to describe pair interactions. The type (pure or mixed) and the number of Nash equilibria affect fundamentally the macroscopic behavior of these systems. In this paper, the general features of Nash equilibria are investigated systematically within the framework of matrix decomposition for n strategies. This approach distinguishes four types of elementary interactions that each possess fundamentally different characteristics. The possible Nash equilibria are discussed separately for different types of interactions and also for their combinations. A relation is established between the existence of infinitely many mixed Nash equilibria and the zero-eigenvalue eigenvectors of the payoff matrix.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.