Modelling Bounded Rationality in Multi-Agent Interactions by Generalized Recursive Reasoning

TL;DR

This paper introduces a hierarchical recursive reasoning framework (GR2) for multi-agent reinforcement learning, modeling agents with varying rationality levels to better reflect real-world decision-making and improve performance.

Contribution

The paper develops a probabilistic graphical model-based hierarchical framework for bounded rationality in MARL, proves equilibrium existence, and provides a convergent actor-critic solver.

Findings

Demonstrates hierarchical thinking in Keynes Beauty Contest

Achieves superior performance over state-of-the-art opponent modeling methods

Validates convergence and effectiveness on multiple MARL benchmarks

Abstract

Though limited in real-world decision making, most multi-agent reinforcement learning (MARL) models assume perfectly rational agents -- a property hardly met due to individual's cognitive limitation and/or the tractability of the decision problem. In this paper, we introduce generalized recursive reasoning (GR2) as a novel framework to model agents with different \emph{hierarchical} levels of rationality; our framework enables agents to exhibit varying levels of "thinking" ability thereby allowing higher-level agents to best respond to various less sophisticated learners. We contribute both theoretically and empirically. On the theory side, we devise the hierarchical framework of GR2 through probabilistic graphical models and prove the existence of a perfect Bayesian equilibrium. Within the GR2, we propose a practical actor-critic solver, and demonstrate its convergent property to a stationary point in two-player games through Lyapunov analysis. On the empirical side, we validate our findings on a variety of MARL benchmarks. Precisely, we first illustrate the hierarchical thinking process on the Keynes Beauty Contest, and then demonstrate significant improvements compared to state-of-the-art opponent modeling baselines on the normal-form games and the cooperative navigation benchmark.