A Risk-Averse Equilibrium for Multi-Agent Systems

Oliver Slumbers, David Henry Mguni, Stephen Marcus McAleer, Jun Wang, Yaodong Yang

Keywords: game theory, safe game theory, risk averse game theory, safe equilibrium, population learning, game theory equilibrium

Abstract: In multi-agent systems, intelligent agents are tasked with making decisions that lead to optimal outcomes when actions of the other agents are as expected, whilst also being prepared for their unexpected behaviour. In this work, we introduce a novel risk-averse solution concept that allows the learner to accommodate low probability actions by finding the strategy with minimum variance, given any level of expected utility. We first prove the existence of such a risk-averse equilibrium, and propose one fictitious-play type learning algorithm for smaller games that enjoys provable convergence guarantees in games classes including zero-sum and potential. Furthermore, we propose an approximation method for larger games based on iterative population-based training that generates a population of risk- averse agents. Empirically, our equilibrium is shown to be able to reduce the utility variance, specifically in the sense that other agents’ low probability behaviour is better accounted for by our equilibrium in comparison to playing other solutions. Importantly, we show that our population of agents that approximate a risk-averse equilibrium is particularly effective against unseen opposing populations, especially in the case of guaranteeing a minimum level of performance, which is critical to safety-aware multi-agent systems.

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TL;DR: We introduce a novel risk-averse solution concept that allows the learner to accommodate low probability actions by finding the strategy with minimum variance, given any level of expected utility.