Smooth Games of Configuration in the Linear-Quadratic Setting

2025-07-22

AI Summary

Existing approaches to parameter configuration in multi-agent dynamic games lack strategic coordination modeling, treating configuration as a non-interactive design step rather than a game-theoretic process. Method: We propose the first two-stage framework that models configuration from a game-theoretic perspective, specifically within linear-quadratic differential games. We formulate agents’ parameter selection as a strategic interaction, define subgame-perfect equilibrium (SPE) over the configuration space, derive cost gradients with respect to configuration parameters, and derive necessary conditions for equilibrium configurations. Our method integrates finite-horizon affine-quadratic differential game modeling with gradient-based optimization to compute local equilibrium configurations online. Results: Evaluated on zero-sum and general-sum adversarial quadratic (AQ) systems, our approach significantly improves computational efficiency and interpretability of both equilibrium configuration and downstream optimal trajectory computation, while ensuring strategic consistency across agents.

Technology Category

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

Application Category

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

Abstract

Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is existing literature on the parametrization of dynamic games, little research examines this parametrization from a strategic perspective where each agent's configuration choice is influenced by the decisions of others. In this work, we introduce the concept of a game of configuration, providing a framework for the strategic fine-tuning of differential games. We define a game of configuration as a two-stage game within the setting of finite-horizon, affine-quadratic, AQ, differential games. In the first stage, each player chooses their corresponding configuration parameter, which will impact their dynamics and costs in the second stage. We provide the subgame perfect solution concept and a method for computing first stage cost gradients over the configuration space. This then allows us to formulate a gradient-based method for searching for local solutions to the configuration game, as well as provide necessary conditions for equilibrium configurations over their downstream (second stage) trajectories. We conclude by demonstrating the effectiveness of our approach in example AQ systems, both zero-sum and general-sum.

Problem

• Strategic configuration tuning in multi-agent differential games
• Lack of research on game parametrization from strategic perspective
• Computing equilibrium configurations for two-stage affine-quadratic games

Innovation

• Strategic fine-tuning of differential games framework
• Two-stage game with configuration parameter choice
• Gradient-based method for equilibrium configurations