The Big Match in Small Space

(Extended Abstract)
  • Kristoffer Arnsfelt Hansen
  • Rasmus Ibsen-Jensen
  • Michal Koucký
Conference paper

DOI: 10.1007/978-3-662-53354-3_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9928)
Cite this paper as:
Hansen K.A., Ibsen-Jensen R., Koucký M. (2016) The Big Match in Small Space. In: Gairing M., Savani R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science, vol 9928. Springer, Berlin, Heidelberg

Abstract

We study repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games with the prototypical example being the Big Match of Gillete (1957). These games may not allow optimal strategies but they always have \(\varepsilon \)-optimal strategies. In this paper we design \(\varepsilon \)-optimal strategies for Player 1 in these games that use only \(O(\log \log T)\) space. Furthermore, we construct strategies for Player 1 that use space s(T), for an arbitrary small unbounded non-decreasing function s, and which guarantee an \(\varepsilon \)-optimal value for Player 1 in the limit superior sense. The previously known strategies use space \(\varOmega (\log T)\) and it was known that no strategy can use constant space if it is \(\varepsilon \)-optimal even in the limit superior sense. We also give a complementary lower bound. Furthermore, we also show that no Markov strategy, even extended with finite memory, can ensure value greater than 0 in the Big Match, answering a question posed by Neyman [11].

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Kristoffer Arnsfelt Hansen
    • 1
  • Rasmus Ibsen-Jensen
    • 2
  • Michal Koucký
    • 3
  1. 1.Aarhus UniversityAarhusDenmark
  2. 2.IST AustriaKlosterneuburgAustria
  3. 3.Charles UniversityPragueCzech Republic

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