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Article Dans Une Revue Journal of Dynamics and Games Année : 2019

A differential game on Wasserstein space. Application to weak approachability with partial monitoring

Résumé

Studying continuous time counterpart of some discrete time dynamics is now a standard and fruitful technique, as some properties hold in both setups. In game theory, this is usually done by considering differential games on Euclidean spaces. This allows to infer properties on the convergence of values of a repeated game, to deal with the various concepts of approachability, etc. In this paper, we introduce a specific but quite abstract differential game defined on the Wasserstein space of probability distributions and we prove the existence of its value. Going back to the discrete time dynamics, we derive results on weak approachability with partial monitoring: we prove that any set satisfying a suitable compatibility condition is either weakly approachable or weakly excludable. We also obtain that the value for differential games with nonanticipative strategies is the same that those defined with a new concept of strategies very suitable to make links with repeated games.

Dates et versions

hal-03089560 , version 1 (28-12-2020)

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Citer

Vianney Perchet, Marc Quincampoix. A differential game on Wasserstein space. Application to weak approachability with partial monitoring. Journal of Dynamics and Games, 2019. ⟨hal-03089560⟩
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