Special Session 41: Dynamics and Games

Convergence to Nash equilibria in monotone games and their characterization
Jarowit Sledzinsk
University of Warsaw, Faculty of Mathematics, Informatics and Mechanics
Poland
Co-Author(s):    
Abstract:
The first AI agent playing the board game Stratego on a human expert level was trained by Regularized Nash Dynamics (R-NaD), an algorithm which converges to Nash equilibria in zero-sum games. Such property of convergence is exceptional - a classical evolutionary game theory replicator dynamics is recurrent in zero-sum games. R-NaD converges to the equilibrium not only in zero-sum games but in a recently introduced wider class of the so-called monotone games. The original definition of the monotone games is difficult to interpret and was not investigated any further than showing it includes zero-sum games and some other known but tight classes. In this talk, we are going to briefly present the ideas behind R-NaD and show our own results concerning monotone games. We formulated a monotonicity-equivalent condition for 2-player games, which is much easier to interpret than the original one. This led us to look closer at the monotone games. We obtained a full classification of games with two strategies and symmetric games with three strategies with respect to pure Nash equilibria.