Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T17:22:42.446Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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