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Stochastic Multiplicative Weights Updates in Zero-Sum Games

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arxiv 2110.02134 v1 pith:V2VAXZNB submitted 2021-10-05 cs.GT cs.MA

James P. Bailey , Sai Ganesh Nagarajan , Georgios Piliouras This is my paper · ORCID
classification cs.GTcs.MA
keywords strategiesagentsweightsmultiplicativestochasticupdatezero-sumagent
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We study agents competing against each other in a repeated network zero-sum game while applying the multiplicative weights update (MWU) algorithm with fixed learning rates. In our implementation, agents select their strategies probabilistically in each iteration and update their weights/strategies using the realized vector payoff of all strategies, i.e., stochastic MWU with full information. We show that the system results in an irreducible Markov chain where agent strategies diverge from the set of Nash equilibria. Further, we show that agents will play pure strategies with probability 1 in the limit.

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  1. Learnable Mixed Nash Equilibria are Collectively Rational

    cs.GT 2025-10 reject novelty 7.0 of 10

    A mixed Nash equilibrium that is locally uniformly stable under uncoupled learning dynamics must be weakly Pareto optimal, and uniform stability controls last-iterate convergence of smoothed best-response dynamics.

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