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Approachability in infinite dimensional spaces. (English) Zbl 1082.91004

Summary: The approachability theorem of D. Blackwell [Pac. J. Math. 6, 1–8 (1956; Zbl 0074.34403)] is extended to infinite dimensional spaces. Two players play a sequential game whose payoffs are random variables. A set \(C\) of random variables is said to be approachable by player 1 if he has a strategy that ensures that the difference between the average payoff and its closest point in \(C\), almost surely converges to zero. Necessary conditions for a set to be approachable are presented.

MSC:

91A05 2-person games
91A20 Multistage and repeated games

Citations:

Zbl 0074.34403
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