Mean-field-type games

Hamidou Tembine

Research output: Contribution to journalArticlepeer-review


This article examines games in which the payoffs and the state dynamics depend not only on the state-action profile of the decision-makers but also on a measure of the state-action pair. These game situations, also referred to as mean-field-type games, involve novel equilibrium systems to be solved. Three solution approaches are presented: (i) dynamic programming principle, (ii) stochastic maximum principle, (iii) Wiener chaos expansion. Relationship between dynamic programming and stochastic maximum principle are established using sub/super weak differentials. In the non-convex control action spaces, connections between the second order weaker differentials of the dual function and second order adjoint processes are provided. Multi-index Wiener chaos expansions are used to transform the non-standard game problems into standard ones with ordinary differential equations. Aggregative and moment-based mean-field-type games are discussed.

Original languageEnglish (US)
Pages (from-to)706-735
Number of pages30
JournalAIMS Mathematics
Issue number4
StatePublished - 2017


  • Coalition
  • Dynamic programming
  • Game theory
  • Maximum principle
  • Mean-field
  • Wiener chaos

ASJC Scopus subject areas

  • General Mathematics


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