Approximate solutions to games of ordered preference

TL;DR

This paper proposes a novel approximation method called lexicographic IBR over time for solving complex receding horizon games of ordered preference, enabling efficient computation of near-optimal solutions in autonomous vehicle scenarios.

Contribution

It introduces a new approximation strategy that reduces complexity growth in solving ordered preference games using receding horizon and iterated best response techniques.

Findings

Efficiently computes approximate solutions in simulated traffic scenarios.

Converges towards generalized Nash equilibria.

Reduces computational complexity compared to existing methods.

Abstract

Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as the time horizon, number of players, or number of preference levels increase. While receding horizon frameworks mitigate long-horizon intractability by solving sequential shorter games, often warm-started, they do not resolve the complexity growth inherent in existing methods for solving games of ordered preference. This paper introduces a solution strategy that avoids excessive complexity growth by approximating solutions using lexicographic iterated best response (IBR) in receding horizon, termed "lexicographic IBR over time." Lexicographic IBR over time uses past information to accelerate convergence. We demonstrate through simulated traffic scenarios that lexicographic IBR over time efficiently computes approximate-optimal solutions for receding horizon games of ordered preference, converging towards generalized Nash equilibria.