Tutorial : Mean Field Stochastic Games

A short version of the tutorial is now available.

Content of the tutorial


  • puceblackShort history, motivations
  • puceblackConnection to mathematical physics, population games, random matrix theory
  • puceblackReplica method, fluid approximation, stochastic approximation
  • puceblackDynamical system approach to large-scale systems
  • puceblackWhat is mean field?
  • puceblackWhy mean field stochastic games?
  • puceblackRelevance in large-scale systems
    • puceblackInternet of things with 2 billions of nodes
    • puceblackNetwork of sensors deployed along a volcano, collecting large quantities of data to monitor seismic activities where transmissions are from relay-node to relay-node until finally delivered to a base station
    • puceblackDisruption-tolerant networks with opportunistic meeting in a large population of 20.000.000 nodes
  • puceblackAdvantages and Limitations of Mean Field Approaches


  • puceblackIntroduction to dynamic games (discrete time, continous time)
    • puceblackEvolutionary games
    • puceblackStochastic games
    • puceblackDifference games
    • puceblackDifferential games
    • puceblackDynamic cooperative games

III-Mean field stochastic game models

  • puceblackDiscrete time models
    • puceblackProbabilistic transitions between states
    • puceblackState evolution described by difference equation or inclusion
  • puceblackContinuous time models
    • puceblackDeterministic state dynamics
    • puceblackStochastic differential equation
    • puceblackImperfect state observation

IV-Asymptotic analysis

    • puceblackMean field convergence
    • puceblackPropagation of chaos and asymptotic indistinguishability per class/type
      • puceblackNon-commutativity in stationary regime, double limit
      • puceblackHow to stabilize a controlled mean field game dynamics?
    • puceblackMean field optimality :Backward-Forward optimality equation
      • puceblackMean field Hamilton-Jacobi-Bellman-Fleming equation
      • puceblackFokker-Planck-Kolmogorov equation
      • puceblackLink with optimal control
      • puceblackBellman-Shapley optimality coupled with Kolmogorov  forward equation
      • puceblackMcKean-Vlasov equations
      • puceblackBackward-forward FPK-McV: existence, uniqueness conditions
    • puceblackMean field equilibria, epsilon-equilibria, population-size dependent approximation, mean field response
      • puceblackSufficiency conditions for Existence of solution
      • puceblackSufficiency conditions for uniqueness of regular solutions (HJBF/FPK-McV)
    • puceblackMean field learning
      • puceblackHybrid learning in large populations
      • puceblackQ-learning for coupled BS-K equations
      • puceblackH-learning for coupled HJBF-K equations


      • puceblackInformation dissemination in opportunistic networks
      • puceblackAccess control in stochastic networks
      • puceblackEvolutionary biology: resource competition and aggregative interaction
      • puceblackPower allocation under log-normal channels
      • puceblackMean field predictor in noisy environment
      • puceblackControlled McKean-Vlasov equations
      • puceblackHow mobility influences the energy consumption in heterogeneous ad hoc networks?
      • puceblackMobility and power saving in wireless networks (link with dynamic stochastic geometry)
      • puceblackMean field dynamics in chemical reaction networks


      • puceblackRisk-sensitive mean field stochastic games: Markov games
        • puceblackMultiplicative Poisson equation, Multiplicative dynamic programming
      • puceblackRisk-sensitive mean field stochastic games: difference games
      • puceblackRisk-sensitive mean field stochastic games: differential games
      • puceblackHybrid mean field stochastic games
      • puceblackRobust mean field stochastic games


Probably very imcomplete.If you think something should be includes, please write me an e-mail.

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