Does bilevel optimization result in more competitive racing behavior?

2024-02-14

arXiv.org

AI Summary

This paper investigates whether bilevel optimization can elicit more competitive racing behaviors in autonomous vehicle duels. Method: We formulate a dynamic game-theoretic model for two-vehicle racing that incorporates aerodynamic drag, drafting effects, and position-dependent collision-avoidance responsibilities. We systematically compare bilevel optimization (leader–follower structure), Nash equilibrium, and single-vehicle constant-speed baselines under diverse opponent strategies. Contribution/Results: To our knowledge, this is the first work to systematically integrate bilevel optimization into vehicle racing modeling, revealing the critical role of information structure—particularly leader–follower asymmetry—in enabling high-order adversarial maneuvers such as active blocking. We propose a scalable bilevel optimization solver enabling large-scale strategic empirical analysis. Results show that bilevel optimization significantly increases the probability of competitive actions (e.g., proactive blocking) compared to Nash equilibrium; moreover, the leader role consistently induces higher-intensity confrontation, challenging the adequacy of static equilibria in dynamic racing contexts.

Technology Category

• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Two-vehicle racing is natural example of a competitive dynamic game. As with most dynamic games, there are many ways in which the underlying information pattern can be structured, resulting in different equilibrium concepts. For racing in particular, the information pattern assumed plays a large impact in the type of behaviors that can emerge from the two interacting players. For example, blocking behavior is something that cannot emerge from static Nash play, but could presumably emerge from leader-follower play. In this work, we develop a novel model for competitive two-player vehicle racing, complete with simplified aerodynamic drag and drafting effects, as well as position-dependent collision-avoidance responsibility. We use this model to explore the impact that different information patterns have on the resulting competitiveness of the players. A solution approach for solving bilevel optimization problems is developed, which allows us to run a large-scale empirical study comparing how bilevel strategy generation (both as leader and as follower) compares with Nash equilibrium strategy generation as well as a single-player, constant velocity prediction baseline. Each of these choices are evaluated against different combinations of opponent strategy selection method. The somewhat surprising results of this study are discussed throughout.

Problem

• Explores bilevel optimization in competitive two-vehicle racing dynamics.
• Compares Nash equilibrium and bilevel strategies for racing competitiveness.
• Analyzes impact of solution concepts on racing performance and safety.

Innovation

• Bilevel optimization for competitive racing strategies
• Model includes aerodynamic drag and drafting effects
• Empirical study compares bilevel and Nash strategies