Inferring Short-Sightedness in Dynamic Noncooperative Games (2412.01017v2)

Abstract: Dynamic game theory is an increasingly popular tool for modeling multi-agent, e.g. human-robot, interactions. Game-theoretic models presume that each agent wishes to minimize a private cost function that depends on others' actions. These games typically evolve over a fixed time horizon, specifying how far into the future each agent plans. In practical settings, however, decision-makers may vary in foresightedness. We conjecture that quantifying and estimating each agent's foresightedness from online data will enable safer and more efficient interactions with other agents. To this end, we frame this inference problem as an \emph{inverse} dynamic game. We consider a specific parametrization of each agent's objective function that smoothly interpolates myopic and farsighted planning. Games of this form are readily transformed into parametric mixed complementarity problems; we exploit the directional differentiability of solutions to these problems with respect to their hidden parameters to solve for agents' foresightedness. We conduct two types of experiments: one with synthetically generated pedestrian motion at a crosswalk and the other with real-world intersection data involving people walking, biking, and driving vehicles. The results of these experiments demonstrate that explicitly inferring agents' foresightedness enables game-theoretic models to more accurately model agents' behavior. Specifically, our results show 33% more accurate prediction of foresighted behavior on average compared to the baseline in real-world scenarios.