Control and optimal stopping Mean Field Games: a linear programming approach

Roxana Dumitrescu, Marcos Leutscher, Peter Tankov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider mean-field game problems where the representative agent chooses both the optimal control and the optimal time to exit the game, where the instantaneous reward function and the coefficients of the state process may depend on the distribution of the other agents. Furthermore, we establish the equivalence between mean-field games equilibria obtained by the linear programming approach and the ones obtained via the controlled/stopped martingale approach, another relaxation method used in earlier papers in the pure control case.

Original languageEnglish
Article number157
JournalElectronic Journal Of Probability
Volume26
DOIs
Publication statusPublished - 2021

Keywords

  • Continuous control
  • Controlled/stopped martingale problem
  • Infinite-dimensional linear programming
  • Mean-field games
  • Optimal stopping
  • Relaxed solutions

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