Abstract
The Nash equilibrium is one of the most central solution concepts to study strategic interactions between multiple players and has recently also been shown to capture sensorimotor interactions between players that are haptically coupled. While previous studies in behavioural economics have shown that systematic deviations from Nash equilibria in economic decision-making can be explained by the more general quantal response equilibria, such deviations have not been reported for the sensorimotor domain. Here we investigate haptically coupled dyads across three different sensorimotor games corresponding to the classic symmetric and asymmetric Prisoner's Dilemma, where the quantal response equilibrium predicts characteristic shifts across the three games, although the Nash equilibrium stays the same. We find that subjects exhibit the predicted deviations from the Nash solution. Furthermore, we show that taking into account subjects' priors for the games, we arrive at a more accurate description of bounded rational response equilibria that can be regarded as a quantal response equilibrium with non-uniform prior. Our results suggest that bounded rational response equilibria provide a general tool to explain sensorimotor interactions that include the Nash equilibrium as a special case in the absence of information processing limitations.
Highlights
Sensorimotor interactions in humans include cooperative examples like carrying a table together across the room or dancing as well as competitive examples like arm wrestling, tug-of-war or playing tennis
We have investigated the concept of quantal response equilibria in human multi-agent interactions in a continuous sensorimotor version of the symmetric and asymmetric
We have tested the hypothesis that quantal response equilibria may provide a more accurate description of stable states of human interaction than the prevailing Nash solution concept
Summary
Sensorimotor interactions in humans include cooperative examples like carrying a table together across the room or dancing as well as competitive examples like arm wrestling, tug-of-war or playing tennis. Several studies have confirmed deviations from Nash equilibria in economic decisionmaking tasks that could be explained by quantal response equilibria [51,52,53], but so far it is unknown whether similar deviations can be observed in sensorimotor interactions To this end, we designed three continuous sensorimotor versions of the traditional two-player matrix game of the Prisoner’s Dilemma [54], corresponding to the classic symmetric form and two asymmetric variations. Assuming that players have limited precision when maximizing expected utility due to bounded rationality, the quantal response equilibria in the asymmetric games differ systematically with the extra cost, even though the Nash equilibrium remains the same This allows for a simple hypothesis test: does behaviour change across the three games or does it stay the same?
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