Symmetric Decomposition of Asymmetric Games

by   Karl Tuyls, et al.

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.


page 1

page 2

page 3

page 4


Insights on the Theory of Robust Games

A robust game is a distribution-free model to handle ambiguity generated...

A Generalised Method for Empirical Game Theoretic Analysis

This paper provides theoretical bounds for empirical game theoretical an...

Evolutionary Game-Theoretical Analysis for General Multiplayer Asymmetric Games

Evolutionary game theory has been a successful tool to combine classical...

For Learning in Symmetric Teams, Local Optima are Global Nash Equilibria

Although it has been known since the 1970s that a globally optimal strat...

An algorithmic solution to the Blotto game using multi-marginal couplings

We describe an efficient algorithm to compute solutions for the general ...

On Skew-Symmetric Games

By resorting to the vector space structure of finite games, skew-symmetr...

Modeling Asymmetric Relationships from Symmetric Networks

Many relationships requiring mutual agreement between pairs of actors pr...