Tractable Equilibrium Computation in Markov Games through Risk Aversion
This addresses the computational bottleneck for principled multi-agent reinforcement learning, offering a tractable solution concept inspired by human decision-making, though it is incremental in applying behavioral economics to existing game theory frameworks.
The paper tackles the intractability of computing Nash equilibria in multi-agent reinforcement learning by introducing risk-averse quantal response equilibria (RQE), which become tractable to compute in n-player matrix and finite-horizon Markov games, with validation showing they capture human play patterns in 2-player games and analysis of sample complexity in Markov games.
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.