Convergence to Nash equilibria in monotone games and their characterization

Speaker(s)

Jarowit Śledziński

Affiliation

MISMAP UW

Language of the talk

English

Date

March 19, 2026, 4:15 p.m.

Room

room 5070

Seminar

Seminar "Mathematics and Physics of Complex Systems"

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It appeared recently that concepts of game theory, Nash equilibrium in particular, are useful in constructing efficient AI agents playing complicated board games. We are going to present Regularized Nash Dynamics (R-NaD), an algorithm that led DeepMind to construct an AI agent winning with humans in the  board game Stratego, while programs from earlier attempts barely reached the amateur level. R-NaD converges to Nash equilibrium and this is a key to the agent's success. The convergence takes place not only in zero-sum games like Stratego but in a whole new introduced class of monotone games. The original definition of the monotone games is difficult to interpret and was not investigated any further than showing it induces zero-sum games and some other known but tight classes. We will present our own work focusing on the exploration of monotone games as a whole class, with most of the results obtained for 2-player games. We have managed to formulate a monotonicity-equivalent condition for 2-player games, which is easier to interpret than the original. This led us to study the class further, which mostly concerns the structure of pure Nash equilibria in symmetric games. Taking advantage of all the above, we perform a full classification of games with two strategies and symmetric games with three strategies with respect to pure Nash equilibria. 

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