Inferring Foresightedness in Dynamic Noncooperative Games
Cade Armstrong, Ryan Park, Xinjie Liu, Kushagra Gupta, David Fridovich-Keil
AI summary
Problem
Existing dynamic game models assume uniform foresight across agents, but real-world decision-makers vary in how they weigh future versus present costs, leading to inaccurate predictions and unsafe interactions.
Approach
The authors model foresight as a time-discounted cost parameter and solve for it via a gradient-based inverse game algorithm that leverages the differentiability of mixed complementarity problem solutions.
Key results
- An explicitly foresighted game formulation with time-discounted costs
- A gradient-based algorithm to infer foresight from online observations
- Over 33% reduction in trajectory error compared to baselines
- Robust performance in partially observable, noisy real-world settings
Why it matters
Enables safer, more efficient multi-agent and human-robot interactions by allowing planners to adapt to how different agents value future consequences.
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 inverse dynamic game. We consider a specific objective function parametrization that smoothly in- terpolates 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 33% more accurate models for agents’ behavior.