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Approachability in infinite dimensional spaces

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  • Ehud Lehrer

    ()
    (School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel)

Abstract

The approachability theorem of Blackwell (1956b) 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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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 31 (2003)
Issue (Month): 2 ()
Pages: 253-268

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Handle: RePEc:spr:jogath:v:31:y:2003:i:2:p:253-268

Note: Received February 2002/Final version July 2002
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Cited by:
  1. Ehud Lehrer & Dinah Rosenberg, 2003. "A Wide Range No-Regret Theorem," Game Theory and Information 0312004, EconWPA.
  2. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
  3. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.

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