IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Special Section on Foundations of Computer Science — Foundations of Computer Science and their New Trends —
Best Possible Algorithms for One-Way Trading with Only the Maximum Fluctuation Ratio Available
ジャーナル フリー

2024 年 E107.D 巻 3 号 p. 278-285


In Variant 4 of the one-way trading game [El-Yaniv, Fiat, Karp, and Turpin, 2001], a player has one dollar at the beginning and wants to convert it to yen only by one-way conversion. The exchange rate is guaranteed to fluctuate between m and M, and only the maximum fluctuation ratio φ = M/m is informed to the player in advance. The performance of an algorithm for this game is measured by the competitive ratio. El-Yaniv et al. derived the best possible competitive ratio over all algorithms for this game. However, it seems that the behavior of the best possible algorithm itself has not been explicitly described. In this paper we reveal the behavior of the best possible algorithm by solving a linear optimization problem. The behavior turns out to be quite different from that of the best possible algorithm for Variant 2 in which the player knows m and M in advance.

© 2024 The Institute of Electronics, Information and Communication Engineers
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