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Algorithms 2010, 3(3), 244-254; doi:10.3390/a3030244

An O(n)-Round Strategy for the Magnus-Derek Game

International University VNU-HCM, Block 6, Linh Trung Ward, Thu Duc District, HCM City, Vietnam
Received: 8 June 2010 / Revised: 6 July 2010 / Accepted: 8 July 2010 / Published: 15 July 2010
(This article belongs to the Special Issue Algorithmic Game Theory)
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We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n – 1) rounds, which is the optimal number of rounds up to a constant factor.
Keywords: algorithmic game theory; additive combinatorics; combinatorial games algorithmic game theory; additive combinatorics; combinatorial games
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nedev, Z. An O(n)-Round Strategy for the Magnus-Derek Game. Algorithms 2010, 3, 244-254.

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