The Parallel Complexity of Coloring Games

Guillaume Ducoffe 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : We wish to motivate the problem of finding decentralized lower-bounds on the complexity of computing a Nash equilibrium in graph games. While the centralized computation of an equilibrium in polynomial time is generally perceived as a positive result, this does not reflect well the reality of some applications where the game serves to implement distributed resource allocation algorithms, or to model the social choices of users with limited memory and computing power. As a case study, we investigate on the parallel complexity of a game-theoretic variation of graph coloring. These " coloring games " were shown to capture key properties of the more general welfare games and Hedonic games. On the positive side, it can be computed a Nash equilibrium in polynomial-time for any such game with a local search algorithm. However, the algorithm is time-consuming and it requires polynomial space. The latter questions the use of coloring games in the modeling of information-propagation in social networks. We prove that the problem of computing a Nash equilibrium in a given coloring game is PTIME-hard, and so, it is unlikely that one can be computed with an efficient distributed algorithm. The latter brings more insights on the complexity of these games.
Type de document :
Communication dans un congrès
Martin Gairing and Rahul Savani. 9th International Symposium, SAGT 2016, Sep 2016, Liverpool, United Kingdom. Springer International Publishing, pp.27-39, 2016, Algorithmic Game Theory. <http://sagt16.csc.liv.ac.uk/>. <10.1007/978-3-662-53354-3_3>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01361056
Contributeur : Guillaume Ducoffe <>
Soumis le : mardi 6 septembre 2016 - 15:40:10
Dernière modification le : vendredi 9 septembre 2016 - 01:05:42
Document(s) archivé(s) le : mercredi 7 décembre 2016 - 13:29:33

Fichier

Duc-SAGT16-finale.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Guillaume Ducoffe. The Parallel Complexity of Coloring Games. Martin Gairing and Rahul Savani. 9th International Symposium, SAGT 2016, Sep 2016, Liverpool, United Kingdom. Springer International Publishing, pp.27-39, 2016, Algorithmic Game Theory. <http://sagt16.csc.liv.ac.uk/>. <10.1007/978-3-662-53354-3_3>. <hal-01361056>

Partager

Métriques

Consultations de
la notice

83

Téléchargements du document

81