Stochastic Multiplicative Weights Updates in Zero-Sum Games

TL;DR

This paper analyzes the behavior of agents using stochastic multiplicative weights updates in repeated zero-sum games, showing convergence to pure strategies and divergence from Nash equilibria.

Contribution

It introduces a stochastic MWU framework with full information in network zero-sum games and characterizes its long-term strategic behavior.

Findings

Agents' strategies form an irreducible Markov chain.

Strategies converge to pure strategies with probability 1.

Agents diverge from Nash equilibria over time.

Abstract

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.