Approachability of Convex Sets in Games with Partial Monitoring |
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Authors: | Vianney Perchet |
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Institution: | 1.équipe Combinatoire et Optimisation, CNRS FRE 3232,Université Pierre et Marie Curie,Paris,France;2.Centre de Mathématiques et de Leurs Applications, CNRS UMR 8536,école Normale Supérieure Cachan,Cachan,France |
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Abstract: | We provide a necessary and sufficient condition under which a convex set is approachable in a game with partial monitoring,
i.e. where players do not observe their opponents’ moves but receive random signals. This condition is an extension of Blackwell’s
Criterion in the full monitoring framework, where players observe at least their payoffs. When our condition is fulfilled,
we construct explicitly an approachability strategy, derived from a strategy satisfying some internal consistency property in an auxiliary game. |
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Keywords: | |
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