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.


    Access

    Download


    Export, share and cite



    Title :

    Symmetric Decomposition of Asymmetric Games


    Contributors:
    Tuyls, K (author) / Perolat, J (author) / Lanctot, M (author) / Ostrovski, G (author) / Savani, R (author) / Leibo, JZ (author) / Ord, T (author) / Graepel, T (author) / Legg, S (author)

    Publication date :

    2018-01-01


    Remarks:

    Scientific Reports , 8 , Article 1015. (2018)


    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English


    Classification :

    DDC:    629



    Combined symmetric/asymmetric vehicle

    SAI QINGSONG / WEI JIANQIU / SAI HONGWEI et al. | European Patent Office | 2016

    Free access

    Feature-weighted categorized play across symmetric games

    Li Calzi M. / Muhlenbernd R. | BASE | 2022

    Free access

    Symmetric and asymmetric flaking processes

    Karna, T. / Jarvinen, E. | British Library Conference Proceedings | 1999


    Dual Symmetric And Asymmetric Mirrors

    Murtaza, S.S. / Srinivasan, A. / Shih, Y.C. et al. | IEEE | 1994


    Dual Symmetric and Asymmetric Mirrors

    IEEE; Lasers and Electro-Optics Society / IEEE; Electron Devices Society | British Library Conference Proceedings | 1994