Physical interaction with a partner plays an essential role in our life experience and is the basis of many daily activities. When two physically coupled humans have different and partly conflicting goals, they face the challenge of negotiating some type of collaboration. This requires that both participants understand their partner’s state and current actions. But, how would the collaboration be affected if information about their partner were unreliable or incomplete? We designed an experiment in which two players (a dyad) are mechanically connected through a virtual spring, but cannot see each other. They were instructed to perform reaching movements with the same start and end position, but through different via-points. In different groups of dyads we varied the amount of information provided to each player about his/her partner: haptic only (the interaction force perceived through the virtual spring), visuo-haptic (the interaction force is also displayed on the screen), and partner visible (in addition to interaction force, partner position is continuously displayed on the screen). We found that incomplete information about the partner affects not only the speed at which collaboration is achieved (less information, slower learning), but also the actual collaboration strategy. In particular, incomplete or unreliable information leads to an interaction strategy characterized by alternating leader-follower roles. Conversely, more reliable information leads to more synchronous behaviors, in which no specific roles can be identified. Simulations based on a combination of game theory and Bayesian estimation suggested that synchronous behaviors correspond to optimal interaction (Nash equilibrium). Roles emerge as sub-optimal forms of interaction, which minimize the need to account for the partner. These findings suggest that collaborative strategies in joint action are shaped by the trade-off between the task requirements and the uncertainty of the information available about the partner.

No abstract

The sense of agency – the subjective feeling of being in control of our own actions – is one central aspect of the phenomenology of action. Computational models provided important contributions toward unveiling the mechanisms underlying the sense of agency in individual action. In particular, the sense of agency is believed to be related to the match between the actual and predicted consequences of our own actions (comparator model). In the study of joint action, models are even more necessary to understand the mechanisms underlying the development of coordination strategies and how the subjective experiences of control emerge during the interaction. In a joint action, we not only need to predict the consequences of our own actions; we also need to predict the actions and intentions of our partner, and to integrate these predictions to infer their joint consequences. Understanding our partner and developing mutually satisfactory coordination strategies are key components of joint action and in the development of the sense of joint agency. Here we discuss a computational architecture which addresses the sense of agency during intentional, real-time joint action. We first reformulate previous accounts of the sense of agency in probabilistic terms, as the combination of prior beliefs about the action goals and constraints, and the likelihood of the predicted movement outcomes. To look at the sense of joint agency, we extend classical computational motor control concepts - optimal estimation and optimal control. Regarding estimation, we argue that in joint action the players not only need to predict the consequences of their own actions, but also need to predict partner’s actions and intentions (a ‘partner model’) and to integrate these predictions to infer their joint consequences. As regards action selection, we use differential game theory – in which actions develop in continuous space and time - to formulate the problem of establishing a stable form of coordination and as a natural extension of optimal control to joint action. The resulting model posits two concurrent observer-controller loops, accounting for ‘joint’ and ‘self’ action control. The two observers quantify the likelihoods of being in control alone or jointly. Combined with prior beliefs, they provide weighing signals which are used to modulate the ‘joint’ and ‘self’ motor commands. We argue that these signals can be interpreted as the subjective sense of joint and self agency. We demonstrate the model predictions by simulating a sensorimotor interactive task where two players are mechanically coupled and are instructed to perform planar movements to reach a shared final target by crossing two differently located intermediate targets. In particular, we explore the relation between self and joint agency and the information available to each player about their partner. The proposed model provides a coherent picture of the inter-relation of prediction, control, and the sense of agency in a broader range of joint actions.

Physical interaction with a partner plays an essential role in our life experience and is 1 the basis of many daily activities. When two physically coupled humans have different 2 and partly conflicting goals, they face the challenge of negotiating some type of 3 collaboration. This requires that both subjects understand their opponent's state and 4 current actions. But, how would the collaboration be affected if information about their 5 opponent were unreliable or incomplete? Here we show that incomplete information 6 about the partner affects not only the speed at which a collaborative strategy is 7 achieved (less information, slower learning), but also the modality of the collaboration. 8In particular, incomplete or unreliable information leads to an interaction strategy 9 characterized by alternating leader-follower roles. In contrast, more reliable information 10 leads to a more synchronous behavior, in which no specific roles can be identified. 11Simulations based on a combination of game theory and Bayesian estimation suggested 12 that synchronous behaviors denote optimal interaction (Nash equilibrium). Roles 13 emerge as sub-optimal forms of interaction, which minimize the need to know about the 14 partner. These findings suggest that physical interaction strategies are shaped by the 15 trade-off of between the task requirements and the uncertainty of the information 16 available about the opponent. 17Author summary 18 Many activities in daily life involve physical interaction with a partner or opponent. In 19 many situations they have conflicting goals. Therefore, they need to negotiate some 20 form of collaboration. Although very common, these situations have rarely been studied 21 empirically. In this study, we specifically address what is a 'optimal' collaboration and 22 how it can be achieved. We also address how developing a collaboration is affected by 23 uncertainty about the partner. Through a combination of empirical studies and 24 computer simulations based on game theory, we show that subject pairs (dyads) are 25 capable of developing stable collaborations, but the learned collaboration strategy 26 depends on the reliability of the information about the partner. High-information dyads 27 converge to the optimal strategies in game-theoretic sense. Low-information dyads 28 converge to strategies that minimize the need to know about the partner. These 29 findings are consistent with a game theoretic learning model which relies on estimates of 30 partner actions, but not partner goals. This similarity sheds some light on the minimal 31 computational machinery which is necessary to an intelligent agent in order to develop 32 stable physical collaborations. 33 July 14, 2018 1/16 36 carrying a load or a therapist interacting with a patient are just the first examples 37 which come to mind. In all these situations, each participant in the interaction needs to 38 know what his/her partner is doing and/or intends to do. On this basis, he/she must 39 then select their own action [1, 2]. To do this, the ...