Average-case competitive analyses for one-way trading

  • Authors:

  • Hiroshi Fujiwara;Kazuo Iwama;Yoshiyuki Sekiguchi

  • Affiliations:

  • Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan 441-8580;School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Faculty of Marine Technology, Tokyo University of Marine Science and Technology, Tokyo, Japan 135-8533

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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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.