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Approachability in infinite dimensional spaces

Author

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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.

Suggested Citation

  • Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 253-268.
    • 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. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    2. 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.
    3. Rad Niazadeh & Negin Golrezaei & Joshua Wang & Fransisca Susan & Ashwinkumar Badanidiyuru, 2023. "Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization," Management Science, INFORMS, vol. 69(7), pages 3797-3817, July.
    4. 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.

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