Mean Field Games and Applications

Guéant, Olivier; Lasry, Jean-Michel; Lions, Pierre Louis

doi:10.1007/978-3-642-14660-2_3

Cited by 512 publications

(491 citation statements)

References 37 publications

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“…⊓ ⊔ An immediate consequence of the above result applies to the case where m is stationary and equal to zero and as such we can drop the last two terms (which depends on m) in the first line of (17). Note that the control strategy is now stationary (we drop explicit dependence on time t).…”

Section: Stabilitymentioning

confidence: 90%

“…Mean field games arise in several applicative domains such as economics, physics, biology, and network engineering (see [1,17,20,22,37]). …”

Section: Introductionmentioning

confidence: 99%

“…Decision problems with mean field coupling terms have also been formalized and studied in [11]. An example from production engineering has been first introduced by [17] (see also [31]). A robust formulation of the production problem is also available in [10].…”

Section: Introductionmentioning

confidence: 99%

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Mean-Field Games and Dynamic Demand Management in Power Grids

Bagagiolo

Bauso

2013

Dyn Games Appl

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This paper applies mean field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At the equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the bang-bang control by introducing a thermostat. Third, we show that the equilibrium is stable in the sense that all agents' states, initially at different values, converge to the equilibrium value or remain confined within a given interval for an opportune initial distribution.

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Section: Stabilitymentioning

confidence: 90%

“…Mean field games arise in several applicative domains such as economics, physics, biology, and network engineering (see [1,17,20,22,37]). …”

Section: Introductionmentioning

confidence: 99%

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Mean-Field Games and Dynamic Demand Management in Power Grids

Bagagiolo

Bauso

2013

Dyn Games Appl

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“…For stochastic mean-field games, uniqueness and existence results were first given by Lasry and Lions (2007a) and Huang et al (2006), with more general results provided in Guéant et al (2011), Cardaliaguet (2012 and Carmona and Delarue (2013). The results in Carmona and Delarue (2013) primarily rely on convexity of the cost functional, and much less is known for mean-field games with concave-convex cost functions.…”

Section: Introductionmentioning

confidence: 99%

Mean-Field Games and Ambiguity Aversion

Huang

2017

SSRN Journal

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This thesis focuses on incorporating the idea of ambiguity aversion into mean-field games.Intuitively, mean-field games describes the dynamics of a system with an infinite population. It is useful in approximating systems with a large population, for which an exact result is computationally intractable. By adding in ambiguity aversion, the mean-field game reflects how players in the population should act if they wish to protect themselves from model misspecification.Two applications of mean-field games are considered through two distinct approaches.The broker execution problem is investigated in a multi-agent framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who search for statistical arbitrage strategies, and (iii) noise traders who buy and sell for exogenous reasons. All optimizing agents (the broker and HFTs) trade against noise traders as well as one another. We use a mean-field game approach to solve the problem and obtain a set of decentralized feedback trading strategies for the major and minor agents. Furthermore, the mean-field game strategies have an N -Nash equilibrium property where N → 0 as N → ∞.The second application focuses on interbank borrowing and lending, which may induce systemic risk into financial markets. A simple model of this is to assume that log-monetary reserves are coupled, and that banks can also borrow/lend from/to a central bank. When all banks optimize their cost of borrowing and lending, this leads to a stochastic game. We account for model uncertainty by recasting the problem as a robust stochastic game and succeed in providing a strategy which leads to a Nash equilibria for ii both the finite game and the mean-field game limit. We prove that an -Nash equilibrium exists and show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.Finally, this thesis develops a modified stochastic maximum principle for min-max problems, and derives new existence and uniqueness results for a mean-field game with ambiguity averse players. An -Nash equilibrium is shown to exist for this class of mean-field games, and the mean-field game equations are explicitly derived in the linearquadratic framework.iii

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“…The mean field approach has been independently developed by J.-M. Lasry and P.-L. Lions in a series of papers see [13] and the references therein using nonlinear PDE's and by M. Huang, P. Caines, Malhamé, see [14] [15] in the setting of stochastic processes, see also [6].…”

Section: Introductionmentioning

confidence: 99%

An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces

Basna¹,

Hilbert²,

Kolokoltsov³

2014

COSA

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Abstract. We investigate mean field games from the point of view of a large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The dynamics of the individual players is governed by pure jump type propagators over a finite space. Investigations are conducted in the framework of non-linear Markov processes. We show that the individual optimal strategy results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players goes to infinity this leads to a jump-type analog of the well-known non-linear McKean-Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The two results combined reveal a 1 N -Nash Equilibrium for the approximating system of N players.

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Mean Field Games and Applications

Abstract: About this text: This text is inspired from a "Cours [21,33].

Cited by 512 publications

References 37 publications

Mean-Field Games and Dynamic Demand Management in Power Grids

Mean-Field Games and Dynamic Demand Management in Power Grids

Mean-Field Games and Ambiguity Aversion

An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces

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