Beating Your Fractional Beatty Game Opponent and: What’s the Question to Your Answer?

Aviezri S. Fraenkel ()
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Aviezri S. Fraenkel: Weizmann Institute of Science, Department of Computer Science and Applied Mathematics

A chapter in Advances in Combinatorics, 2013, pp 175-186 from Springer

Abstract: Abstract Given a subtraction game on two piles of tokens, the usual question is to characterize its P-positions. These normally split the positive integers into two complementary sequences for Wythoff-like games. Here we invert the problem: We are given two sequences, and the challenge is to find appropriate succinct game rules for a game having the given P-positions. The main additional challenge in this work is that the given sequences do not split the positive integers. We present two solutions for a seemingly first such problem, the second in terms of two exotic numeration systems. Both characterizations lead to linear-time winning strategies for the game induced by the two sequences.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-30979-3_9

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DOI: 10.1007/978-3-642-30979-3_9

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