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Nature Scientific Reports
Researchers at the University of Liverpool have had a paper published in the prestigious journal Nature, Scientific Reports. The paper is authored by members of the Department of Computer Science at the University of Liverpool, Karl Tuyls and Rahul Savani, together with collaborators at Google DeepMind and the University of Oxford. The title of the paper is "Symmetric Decomposition of Asymmetric Games" and a synopsis is given below.
Analysing multiagent interactions using evolutionary dynamics provides not only valuable insights into the (Nash) equilibria and their stability, but also sheds light on the behaviour trajectories of the involved agents. As such it can be a very useful tool to analyse the Nash structure and dynamics of several interacting (and learning) agents in a multiagent system. However, when dealing with asymmetric games the analysis quickly becomes tedious, as in this case we have a coupled system of replicator equations, and changes in the behaviour of one agent immediately change the dynamics in the linked replicator equation describing the behaviour of the other agent, and vice versa. This paper sheds new light on asymmetric games, and reveals a number of theorems that allow for a more elegant analysis of asymmetric multiagent games. The presented theory allows to identify the Nash structure of the asymmetric game by investigating the simpler symmetric counterparts, seriously reducing the complexity of the analysis. The complexity stems from the fact that when using the evolutionary dynamics of an asymmetric game to analyse its equilibrium structure, the dynamics for the players are intrinsically coupled and high-dimensional. While one could fix a player's strategy and consider the induced dynamics for the other player in its respective strategy simplex, a static trajectory plot of this would not faithfully represent the complexity of the full two-player dynamics, and as such analysis becomes very difficult. Our results overcome this problem allowing to identify Nash equilibria of the asymmetric game by examining the much simpler counterpart games.