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Roxana Dumitrescu (King's college, Londres)

Optimal Stopping mean-field games and applications to electricity markets

Abstract: In this talk, I present recent results on 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 the optimal time to exit the game, and we show the existence of an equilibria and provide some uniqueness results. Furthermore, we establish the equivalence between mean-field games equilibria obtained by the linear programming approach and the ones obtained via other approaches used in the previous literature. We then present a fictious play algorithm to approximate the mean-field game population dynamics in the context of the linear programming approach. Finally, we give an application of the theoretical and numerical contributions introduced in the first part of the talk to an entry-exit game in electricity markets. The talk is based on several works, joint with R. Aïd, G. Bouveret, M. Leutscher and P. Tankov.

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