Risk-sensitive mean-field-type games with Lp-norm drifts

Research output: Contribution to journalArticle

Abstract

Abstract We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean-Vlasov dynamics.

Original languageEnglish (US)
Article number6454
Pages (from-to)224-237
Number of pages14
JournalAutomatica
Volume59
DOIs
StatePublished - Jan 1 2015

Fingerprint

Maximum principle
Dynamic programming
Chaos theory
Decision making

Keywords

  • Game theory
  • Mean-field
  • Risk-sensitive

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Risk-sensitive mean-field-type games with Lp-norm drifts. / Hamidou, Tembine.

In: Automatica, Vol. 59, 6454, 01.01.2015, p. 224-237.

Research output: Contribution to journalArticle

@article{15ec83152ee84c39af778490fa029eb6,
title = "Risk-sensitive mean-field-type games with Lp-norm drifts",
abstract = "Abstract We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean-Vlasov dynamics.",
keywords = "Game theory, Mean-field, Risk-sensitive",
author = "Tembine Hamidou",
year = "2015",
month = "1",
day = "1",
doi = "10.1016/j.automatica.2015.06.036",
language = "English (US)",
volume = "59",
pages = "224--237",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Risk-sensitive mean-field-type games with Lp-norm drifts

AU - Hamidou, Tembine

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Abstract We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean-Vlasov dynamics.

AB - Abstract We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean-Vlasov dynamics.

KW - Game theory

KW - Mean-field

KW - Risk-sensitive

UR - http://www.scopus.com/inward/record.url?scp=84937953908&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937953908&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2015.06.036

DO - 10.1016/j.automatica.2015.06.036

M3 - Article

AN - SCOPUS:84937953908

VL - 59

SP - 224

EP - 237

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 6454

ER -