2024/10/28 by Dong Ho Lee, Lasse Peters, Lee, Dong Ho +3 · 1 voice · 1 citation
Computer Science · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #Economic Theory and Institutions #FOS: Computer and information sciences #Multiagent Systems (cs.MA) #cs.GT #cs.MA
paper · pdf · doi:10.48550/arxiv.2410.21447
openalex publication_date 2024/10/28 · arxiv published 2024/10/28 · arxiv updated 2025/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.