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

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Lee, Dong Ho, Peters, Lasse, Fridovich-Keil, David
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866911037516677120
author Lee, Dong Ho
Peters, Lasse
Fridovich-Keil, David
author_facet Lee, Dong Ho
Peters, Lasse
Fridovich-Keil, David
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_21447
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle You Can't Always Get What You Want: Games of Ordered Preference
Lee, Dong Ho
Peters, Lasse
Fridovich-Keil, David
Computer Science and Game Theory
Multiagent Systems
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.
title You Can't Always Get What You Want: Games of Ordered Preference
topic Computer Science and Game Theory
Multiagent Systems
url https://arxiv.org/abs/2410.21447