Computational joint action: dynamical models to understand the development of joint coordination

Coordinating with others is part of our everyday experience. Previous studies using sensorimotor coordination games suggest that human dyads develop coordination strategies that can be interpreted as Nash equilibria. However, if the players are uncertain about what their partner is doing, they develop coordination strategies which are robust to the actual partner’s actions. This has suggested that humans select their actions based on an explicit prediction of what the partner will be doing – a partner model – which is probabilistic by nature. However, the mechanisms underlying the development of a joint coordination over repeated trials remain unknown. Very much like sensorimotor adaptation of individuals to external perturbations (eg force fields or visual rotations), dynamical models may help to understand how joint coordination develops over repeated trials.

Here we present a general computational model – based on game theory and Bayesian estimation – designed to understand the mechanisms underlying the development of a joint coordination over repeated trials. Joint tasks are modeled as quadratic games, where each participant’s task is expressed as a quadratic cost function. Each participant predicts their partner’s next move (partner model) by optimally combining predictions and sensory observations, and selects their actions through a stochastic optimization of its expected cost, given the partner model. The model parameters include perceptual uncertainty (sensory noise), partner representation (retention rate and process noise), uncertainty in action selection and its rate of decay (which can be interpreted as the action’s learning rate). The model can be used in two ways: (i) to simulate interactive behaviors, thus helping to make specific predictions in the context of a given joint action scenario; and (ii) to analyze the action time series in actual experiments, thus providing quantitative metrics that describe individual behaviors during an actual joint action.

We demonstrate the model in a variety of joint action scenarios. In a sensorimotor version of the Stag Hunt game, the model predicts that different representations of the partner lead to different Nash equilibria. In a joint two via-point (2-VP) reaching task, in which the actions consist of complex trajectories, the model captures well the observed temporal evolution of performance. For this task we also estimated the model parameters from experimental observations, which provided a comprehensive characterization of individual dyad participants.

Computational models of joint action may help identifying the factors preventing or facilitating the development of coordination. They can be used in clinical settings, to interpret the observed behaviors in individuals with impaired interaction capabilities. They may also provide a theoretical basis to devise artificial agents that establish forms of coordination that facilitate neuromotor recovery.

Author summary

Acting together (joint action) is part of everyday experience. But, how do we learn to coordinate with others and collaborate? Using a combination of experiments and computational models we show that through multiple repetitions of the same joint task we select the action which represents the ‘best response’ to what we believe our opponent will do. Such a belief about our partner (partner model) is developed gradually, by optimally combining prior assumptions (how repeatable or how erratic our opponent behaves) with sensory information about our opponent’s past actions. Rooted in game theory and Bayesian estimation, the model accounts for the development of the mutual ‘trust’ among partners which is essential for establishing a mutually advantageous collaboration, and explains how we combine decisions and movements in complex coordination scenarios. The model can be used as a generative tool, to simulate the development of coordination in a specific joint action scenario, and as an analytic tool to characterize the individual traits or defects in the ability to establish collaborations.