Approachability of Convex Sets in Games with Partial Monitoring

Vianney Perchet ()
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Vianney Perchet: Université Pierre et Marie Curie

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 3, No 13, 665-677

Abstract: 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. We also provide an example of a convex set, that is neither (weakly)-approachable nor (weakly)-excludable, a situation that cannot occur in the full monitoring case. We finally apply our result to describe an ε-optimal strategy of the uninformed player in a zero-sum repeated game with incomplete information on one side.

Keywords: Repeated games; Blackwell approachability; Partial monitoring; Convex sets; Incomplete information (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-011-9797-3

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