Tractable Equilibrium Computation in Markov Games through Risk Aversion

TL;DR

This paper introduces a computationally feasible class of risk-averse equilibrium concepts for multi-agent games, inspired by human decision-making, which can be efficiently computed and better reflect observed behaviors.

Contribution

It proposes risk-averse quantal response equilibria that are tractable to compute in all n-player Markov games, independent of game structure, and aligns with human play patterns.

Findings

Risk-averse equilibria are computationally tractable in all n-player Markov games.

The proposed equilibria capture human decision-making patterns in experimental games.

Sample complexity analysis shows efficient computation in finite-horizon Markov games.

Abstract

A significant roadblock to the development of principled multi-agent reinforcement learning is the fact that desired solution concepts like Nash equilibria may be intractable to compute. To overcome this obstacle, we take inspiration from behavioral economics and show that -- by imbuing agents with important features of human decision-making like risk aversion and bounded rationality -- a class of risk-averse quantal response equilibria (RQE) become tractable to compute in all $n$-player matrix and finite-horizon Markov games. In particular, we show that they emerge as the endpoint of no-regret learning in suitably adjusted versions of the games. Crucially, the class of computationally tractable RQE is independent of the underlying game structure and only depends on agents' degree of risk-aversion and bounded rationality. To validate the richness of this class of solution concepts we show that it captures peoples' patterns of play in a number of 2-player matrix games previously studied in experimental economics. Furthermore, we give a first analysis of the sample complexity of computing these equilibria in finite-horizon Markov games when one has access to a generative model and validate our findings on a simple multi-agent reinforcement learning benchmark.