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

In: Advances in Combinatorics

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  • Aviezri S. Fraenkel

    (Weizmann Institute of Science, Department of Computer Science and Applied Mathematics)

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.

Suggested Citation

  • Aviezri S. Fraenkel, 2013. "Beating Your Fractional Beatty Game Opponent and: What’s the Question to Your Answer?," Springer Books, in: Ilias S. Kotsireas & Eugene V. Zima (ed.), Advances in Combinatorics, edition 127, pages 175-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-30979-3_9
    DOI: 10.1007/978-3-642-30979-3_9
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