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Average-Case Competitive Analyses for One-Way Trading

  • Hiroshi Fujiwara
  • Kazuo Iwama
  • Yoshiyuki Sekiguchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m,M]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum rate m. El-Yaniv et al presented the optimal worst-case threat-based strategy (WTB) for this game [4].In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal algorithms for each of them. Remarkable differences in behavior are as follows: Unlike other algorithms, the average-case threat-based strategy (ATB) that minimizes \(E[\text{OPT} / \text{ALG}]\) exchanges little by little. The maximization of \(E [\text{ALG} / \text{OPT}]\) and the minimization of \(E [\text{OPT}] / E [\text{ALG}]\) lead to similar algorithms in that both exchange all at once. However, their timing is different.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hiroshi Fujiwara
    • 1
  • Kazuo Iwama
    • 2
  • Yoshiyuki Sekiguchi
    • 3
  1. 1.Department of InformaticsKwansei Gakuin UniversitySandaJapan
  2. 2.School of InformaticsKyoto University, Yoshida-HonmachiKyotoJapan
  3. 3.Faculty of Marine TechnologyTokyo University of Marine Science and TechnologyTokyoJapan

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