Nash Equilibria in Multi-Agent Motor Interactions

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.Author Summary: Human motor interactions range from adversarial activities like judo and arm wrestling to more cooperative activities like tandem riding and tango dancing. In this study, we design a new methodology to study human sensorimotor interactions quantitatively based on game theory. We develop two motor tasks based on the prisoner's dilemma and the rope-pulling game in which we introduce an intrinsic cost related to effort rather than the typical monetary outcome used in cognitive game theory. We find that continuous motor interactions converged to game theoretic outcomes similar to the interaction dynamics reported for other dynamical systems in biology ranging in scale from microorganisms to population dynamics.