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WINNING AN INFINITE COMBINATION OF GAMES

Part of:Game theory

Published online by Cambridge University Press:  24 February 2012

Nathan Bowler
Nathan Bowler*
Affiliation:
Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany (email: N.Bowler1729@gmail.com)

Abstract

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We introduce a precise framework for transferring strategies from simpler to more complex games, and use it to construct strategies in certain finite and infinite combinations of games. In particular, we give a finitary characterization of finite hypergraphs X such that the first player can win the positional game on infinitely many copies of X. This resolves a conjecture of Leader.

MSC classification

Secondary:91A46: Combinatorial games

Information

Type
Research Article
Information
Mathematika , Volume 58 , Issue 2 , July 2012, pp. 419 - 431
Copyright
Copyright © University College London 2012

References

[1]Beck, J., Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications 114), Cambridge University Press (Cambridge, 2008).CrossRefGoogle Scholar
[2]Bowler, N., A unified approach to the construction of categories of games. PhD Thesis, University of Cambridge, 2011.Google Scholar
[3]Conway, J. H., On Numbers and Games, 2nd edn, A K Peters (Natick, MA, 2001).Google Scholar
[4]Leader, I. B., Hypergraph games. Lecture notes, available at http://tartarus.org/gareth/maths/notes/, 2008.Google Scholar