Linear-quadratic risk-sensitive mean field games

Jun Moon, Tamer Basar

Research output: Contribution to journalConference articlepeer-review


In this paper, we consider linear-quadratic risk-sensitive mean field games (LQRSMFGs). Each agent strives to minimize an exponentiated integral quadratic cost or risk-sensitive cost function, which is coupled with other agents via a mean field term. By invoking the Nash certainty equivalence principle, we first obtain a robust decentralized control law for each agent to construct a mean field system. We then provide appropriate conditions under which the mean field system admits a unique deterministic function that approximates the mean field term with arbitrarily small error when the number of agents, say N, goes to infinity. We also show the closed-loop system stability, and prove that the set of N robust decentralized control laws possesses an ε-Nash equilibrium property. Moreover, we show that ε can be taken to be arbitrarily close to zero as N → ∞, but our ε bound is weaker than its linear-quadratic mean field game (LQMFG) counterpart due to risk-sensitivity in the present case. Finally, we discuss two different limiting cases, and show that one of these is equivalent to the corresponding LQMFG.

Original languageEnglish (US)
Article number7039801
Pages (from-to)2691-2696
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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