Mean Field Games with Singular Controls of Bounded Velocity

Guo, Xin; Lee, Joon Seok

doi:10.2139/ssrn.2932277

Cited by 5 publications

(11 citation statements)

References 43 publications

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“…This system of variational inequalities is the characterization of a saddle point of (22). From this observation we deduce the following : Theorem 2.5.…”

Section: The Optimal Control Interpretationmentioning

confidence: 76%

“…From this observation we deduce the following : Theorem 2.5. The unique minimizer of (22) is the density of players m of the MFG of impulse control. This is if (u, m) is the solution of (21) given by theorem 2.4, then m is the unique minimizer of (22).…”

Section: The Optimal Control Interpretationmentioning

confidence: 99%

“…Concerning closely related works, several optimal control problems, related to the impulse control problem, have been studied in a MFG setting. Optimal stopping or obstacle problems have been studied in [5,18,30,15], singular controls in [16,22] and optimal switching in [19]. 1.2.…”

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confidence: 99%

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Fokker-Planck equations of jumping particles and mean field games of impulse control

Bertucci¹

2018

Preprint

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This paper is interested in the description of the density of particles evolving according to some optimal policy of an impulse control problem. We first fix sets on which the particles jump and explain how we can characterize such a density. We then investigate the coupled case in which the underlying impulse control problem depends on the density we are looking for : the mean field game of impulse control. In both cases, we give a variational characterization of the densities of jumping particles.

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“…This system of variational inequalities is the characterization of a saddle point of (22). From this observation we deduce the following : Theorem 2.5.…”

Section: The Optimal Control Interpretationmentioning

confidence: 76%

Section: The Optimal Control Interpretationmentioning

confidence: 99%

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Fokker-Planck equations of jumping particles and mean field games of impulse control

Bertucci¹

2018

Preprint

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“…In the singular control setting where controls are càdlàg type, [16] explicitly solved the N -player game and MFG of a classical fuel followers problem. The -NE approximation of MFGs was first established for regular controls in [9,10] with = 1 N and then for singular controls in [16] and [14] with = 1 √ N . Our result with = 1 √ N for impulse controls is consistent with those for singular controls as both allow discontinuity in the state space.…”

Section: Introductionmentioning

confidence: 99%

Nonzero-sum stochastic games and mean-field games with impulse controls

Basei¹,

Cao²,

Guo³

2019

Preprint

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We consider a general class of nonzero-sum N -player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limit situation of N → ∞, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, the MFG is an -NE approximation to the N -player game, with = O 1 √ N . As an example, we analyze in details a class of stochastic games which extends the classical cash management problem to the game setting. In particular, we characterize the NEs for its two-player case and compare the results to the single-player case, showing the impact of competition on the player's optimal strategy, with sensitivity analysis of the model parameters.

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“…The recent paper[13] only considers absolutely continuous singular controls. Our notion of singular controls is more general.…”

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confidence: 99%