Approachability in infinite dimensional spaces

Approachability in infinite dimensional spaces

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Article ID: iaor20033277
Country: Germany
Volume: 31
Issue: 2
Start Page Number: 253
End Page Number: 268
Publication Date: Jan 2002
Journal: International Journal of Game Theory
Authors:
Abstract:

The approachability theorem of Blackwell 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.

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