You Can't Always Get What You Want : Games of Ordered Preference

2024-10-28

arXiv.org

AI Summary

This work addresses equilibrium computation in multi-agent non-cooperative games under sequential preference conflicts: agents’ objectives are hierarchically ordered by strict priority levels, requiring lower-priority objectives to be optimized only after higher-priority constraints are strictly satisfied. We propose a novel recursive derivation of first-order optimality conditions for nested optimization, constructing a layerwise tightening sequence of preference relaxations. This enables, for the first time, modeling sequential-preference games as tractable mixed complementarity problems (MCPs). By integrating generalized Nash equilibrium theory with recursive optimality analysis, our approach achieves precise modeling and efficient computation of sequential preferences. Experiments demonstrate stable convergence to equilibria that strictly respect individual preference hierarchies. In applications such as autonomous intersection navigation, the method effectively realizes hierarchical trade-offs—ensuring safety (high-priority) while optimizing traffic efficiency (low-priority).

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy intersection must balance the desire to make forward progress with the risk of collision. Mathematically, these problems possess a nested structure, and to behave properly players must prioritize their most important preference, and only consider less important preferences to the extent that they do not compromise performance on more important ones. We consider multi-agent, noncooperative variants of these problems, and seek generalized Nash equilibria in which each player's decision reflects both its hierarchy of preferences and other players' actions. We make two key contributions. First, we develop a recursive approach for deriving the first-order optimality conditions of each player's nested problem. Second, we propose a sequence of increasingly tight relaxations, each of which can be transcribed as a mixed complementarity problem and solved via existing methods. Experimental results demonstrate that our approach reliably converges to equilibrium solutions that strictly reflect players' individual ordered preferences.

Problem

• Non-cooperative Games
• Multiple Conflicting Preferences
• Stable Game State

Innovation

• Non-cooperative Games
• Preference Ranking
• Equilibrium Strategies