Nash equilibria in human sensorimotor interactions explained by Q-learning with intrinsic costs

Abstract

The Nash equilibrium concept has previously been shown to be an important tool to understand human sensorimotor interactions, where different actors vie for minimizing their respective effort while engaging in a multi-agent motor task. However, it is not clear how such equilibria are reached. Here, we compare different reinforcement learning models to human behavior engaged in sensorimotor interactions with haptic feedback based on three classic games, including the prisoner’s dilemma, and the symmetric and asymmetric matching pennies games. We find that a discrete analysis that reduces the continuous sensorimotor interaction to binary choices as in classical matrix games does not allow to distinguish between the different learning algorithms, but that a more detailed continuous analysis with continuous formulations of the learning algorithms and the game-theoretic solutions affords different predictions. In particular, we find that Q-learning with intrinsic costs that disfavor deviations from average behavior explains the observed data best, even though all learning algorithms equally converge to admissible Nash equilibrium solutions. We therefore conclude that it is important to study different learning algorithms for understanding sensorimotor interactions, as such behavior cannot be inferred from a game-theoretic analysis alone, that simply focuses on the Nash equilibrium concept, as different learning algorithms impose preferences on the set of possible equilibrium solutions due to the inherent learning dynamics.