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Average-case competitive analyses for one-way trading

Author

Listed:
  • Hiroshi Fujiwara

    (Toyohashi University of Technology)

  • Kazuo Iwama

    (Kyoto University)

  • Yoshiyuki Sekiguchi

    (Tokyo University of Marine Science and Technology)

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 for this game (El-Yaniv et al. 2001). 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 strategies for each of them. Remarkable differences in behavior are as follows: Unlike other strategies, the average-case threat-based strategy that minimizes E[OPT/ALG] exchanges little by little. The maximization of E[ALG/OPT] and the minimization of E[OPT]/E[ALG] lead to similar strategies in that both exchange all at once. However, their timing is different. We also prove minimax theorems with respect to each objective function.

Suggested Citation

  • Hiroshi Fujiwara & Kazuo Iwama & Yoshiyuki Sekiguchi, 2011. "Average-case competitive analyses for one-way trading," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 83-107, January.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:1:d:10.1007_s10878-009-9239-4
    DOI: 10.1007/s10878-009-9239-4
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    References listed on IDEAS

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    1. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.
    2. Luca Becchetti & Stefano Leonardi & Alberto Marchetti-Spaccamela & Guido Schäfer & Tjark Vredeveld, 2006. "Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 85-108, February.
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    Cited by:

    1. Wenming Zhang & Ye Zhang & Yongxi Cheng & Shankui Zheng, 2022. "An online trading problem with an increasing number of available products," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 518-531, August.
    2. Wang, Liying & Lan, Yingjie & Zhang, Jean X., 2016. "Competitive difference analysis of the one-way trading problem with limited informationAuthor-Name: Wang, Wei," European Journal of Operational Research, Elsevier, vol. 252(3), pages 879-887.

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