Quantifying cooperation between artificial agents using synergistic information

When designing interactive human-machine sys-tems, it is often assumed that it is desirable for such systems to behave cooperatively towards a human operator in order to improve trust, acceptance, and usability, but also to increase task efficiency. To design cooperative human-machine interaction (HMI) systems, we have to be able to define and quantitatively describe cooperative behavior, for example, to control, optimize, or evaluate the interaction. Despite the increased interest in cooperative HMI in recent years, an approach that provides a suitable definition of cooperation and also a method for its quantification is still missing. In the present work, we therefore develop a novel definition of cooperative behavior in HMI contexts, based on which we propose to quantify cooperation using recent methods from information theory. We define cooperation as joint, coordinated actions that are mutually adapted such as to facilitate the realization of a goal. Thus, cooperation is characterized by a synergistic effect of joint actions towards the goal. Here, we propose to quantify cooperation using the recently introduced partial information decomposition framework from information theory, which proposes measures to quantify the synergistic contributions of two inputs to a target variable. In particular, we propose to apply the synergy measure to two or more input variables describing agents' actions towards a target variable that describes the current goal state. As a first validation, we applied our approach in a grid-world environment, in which two agents solve a cooperative foraging task. We found that synergy was higher for agents implementing cooperative strategies compared to baseline and non-cooperative strategies, and we found higher synergy in trials with high numbers of cooperative actions. We conclude that the synergy is a promising candidate measure for identifying cooperative behavior in goal-oriented interactions.