Hypergraph conditions for the solvability of the ergodic equation for zero-sum games

Marianne Akian; Stéphane Gaubert; Antoine Hochart

doi:10.1109/CDC.2015.7403138

Hypergraph conditions for the solvability of the ergodic equation for zero-sum games

Marianne Akian
, Stéphane Gaubert
, Antoine Hochart

Ecole polytechnique

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

2 Citations (Scopus)

Résumé

The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optimal stationary strategies are readily obtained from its solution. In this paper, we give a general sufficient condition for the solvability of the ergodic equation, for a game with finite state space but arbitrary action spaces. This condition involves a pair of directed hypergraphs depending only on the growth at infinity of the Shapley operator of the game. This refines a recent result of the authors which only applied to games with bounded payments, as well as earlier nonlinear fixed point results for order preserving maps, involving graph conditions.

langue originale	Anglais
titre	54rd IEEE Conference on Decision and Control,CDC 2015
Editeur	Institute of Electrical and Electronics Engineers Inc.
Pages	5845-5850
Nombre de pages	6
ISBN (Electronique)	9781479978861
Les DOIs	https://doi.org/10.1109/CDC.2015.7403138
état	Publié - 8 févr. 2015
Evénement	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japon Durée: 15 déc. 2015 → 18 déc. 2015

Série de publications

Nom	Proceedings of the IEEE Conference on Decision and Control
ISSN (imprimé)	0743-1546
ISSN (Electronique)	2576-2370

Une conférence

Une conférence	54th IEEE Conference on Decision and Control, CDC 2015
Pays/Territoire	Japon
La ville	Osaka
période	15/12/15 → 18/12/15

Accès au document

10.1109/CDC.2015.7403138

Contient cette citation

Akian, M., Gaubert, S., & Hochart, A. (2015). Hypergraph conditions for the solvability of the ergodic equation for zero-sum games. Dans 54rd IEEE Conference on Decision and Control,CDC 2015 (p. 5845-5850). Article 7403138 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403138

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title = "Hypergraph conditions for the solvability of the ergodic equation for zero-sum games",

abstract = "The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optimal stationary strategies are readily obtained from its solution. In this paper, we give a general sufficient condition for the solvability of the ergodic equation, for a game with finite state space but arbitrary action spaces. This condition involves a pair of directed hypergraphs depending only on the growth at infinity of the Shapley operator of the game. This refines a recent result of the authors which only applied to games with bounded payments, as well as earlier nonlinear fixed point results for order preserving maps, involving graph conditions.",

keywords = "Zero-sum games, computational methods, directed hypergraphs, ergodic control, nonlinear consensus, risk-sensitive control, stochastic control",

author = "Marianne Akian and St{\'e}phane Gaubert and Antoine Hochart",

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Akian, M , Gaubert, S & Hochart, A 2015, Hypergraph conditions for the solvability of the ergodic equation for zero-sum games. Dans 54rd IEEE Conference on Decision and Control,CDC 2015., 7403138, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., p. 5845-5850, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japon, 15/12/15. https://doi.org/10.1109/CDC.2015.7403138

Hypergraph conditions for the solvability of the ergodic equation for zero-sum games. / Akian, Marianne ; Gaubert, Stéphane; Hochart, Antoine.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 5845-5850 7403138 (Proceedings of the IEEE Conference on Decision and Control).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - Hypergraph conditions for the solvability of the ergodic equation for zero-sum games

AU - Akian, Marianne

AU - Gaubert, Stéphane

AU - Hochart, Antoine

PY - 2015/2/8

Y1 - 2015/2/8

N2 - The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optimal stationary strategies are readily obtained from its solution. In this paper, we give a general sufficient condition for the solvability of the ergodic equation, for a game with finite state space but arbitrary action spaces. This condition involves a pair of directed hypergraphs depending only on the growth at infinity of the Shapley operator of the game. This refines a recent result of the authors which only applied to games with bounded payments, as well as earlier nonlinear fixed point results for order preserving maps, involving graph conditions.

AB - The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optimal stationary strategies are readily obtained from its solution. In this paper, we give a general sufficient condition for the solvability of the ergodic equation, for a game with finite state space but arbitrary action spaces. This condition involves a pair of directed hypergraphs depending only on the growth at infinity of the Shapley operator of the game. This refines a recent result of the authors which only applied to games with bounded payments, as well as earlier nonlinear fixed point results for order preserving maps, involving graph conditions.

KW - Zero-sum games

KW - computational methods

KW - directed hypergraphs

KW - ergodic control

KW - nonlinear consensus

KW - risk-sensitive control

KW - stochastic control

U2 - 10.1109/CDC.2015.7403138

DO - 10.1109/CDC.2015.7403138

M3 - Conference contribution

AN - SCOPUS:84962010435

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5845

EP - 5850

BT - 54rd IEEE Conference on Decision and Control,CDC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

Y2 - 15 December 2015 through 18 December 2015

ER -

Hypergraph conditions for the solvability of the ergodic equation for zero-sum games

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