Inferring Foresightedness in Dynamic Noncooperative Games

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, or how much they care about their current cost in relation to their past and future costs. 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inverse</i> dynamic game. We consider a specific objective function parametrization 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 three experiments: one with synthetically generated delivery robot motion, one with real-world data involving people walking, biking, and driving vehicles, and one using high-fidelity simulators. The results of these experiments demonstrate that explicitly inferring agents' foresightedness enables game-theoretic models to make <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bf {33\%}$</tex-math></inline-formula> more accurate models for agents' behavior.