Tuyls, K;
Perolat, J;
Lanctot, M;
Ostrovski, G;
Savani, R;
Leibo, JZ;
Ord, T;
... Legg, S; + view all
(2018)
Symmetric Decomposition of Asymmetric Games.
Scientific Reports
, 8
, Article 1015. 10.1038/s41598-018-19194-4.
Preview |
Text
s41598-018-19194-4.pdf - Published Version Download (3MB) | Preview |
Abstract
We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be decomposed into its symmetric counterparts by envisioning and investigating the payoff tables (A and B) that constitute the asymmetric game, as two independent, single population, symmetric games. We reveal several surprising formal relationships between an asymmetric two-population game and its symmetric single population counterparts, which facilitate a convenient analysis of the original asymmetric game due to the dimensionality reduction of the decomposition. The main finding reveals that if (x,y) is a Nash equilibrium of an asymmetric game (A,B), this implies that y is a Nash equilibrium of the symmetric counterpart game determined by payoff table A, and x is a Nash equilibrium of the symmetric counterpart game determined by payoff table B. Also the reverse holds and combinations of Nash equilibria of the counterpart games form Nash equilibria of the asymmetric game. We illustrate how these formal relationships aid in identifying and analysing the Nash structure of asymmetric games, by examining the evolutionary dynamics of the simpler counterpart games in several canonical examples.
| Type: | Article |
|---|---|
| Title: | Symmetric Decomposition of Asymmetric Games |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1038/s41598-018-19194-4 |
| Publisher version: | http://dx.doi.org/10.1038/s41598-018-19194-4 |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2018. 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 license, and indicate if changes were made. Te images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10043496 |
Archive Staff Only
 |
View Item |
