Algorithms for lattice games

Alan Guo () and Ezra Miller ()

International Journal of Game Theory, 2013, vol. 42, issue 4, 777-788

Abstract: This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games (Guo et al. Oberwolfach Rep 22: 23–26, 2009 ; Guo and Miller, Adv Appl Math 46:363–378, 2010 ). Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a given position is a winning position, and to find a move to a winning position, if not; and (ii) to decide whether two given positions are congruent, in the sense of misère quotient theory (Plambeck, Integers, 5:36, 2005 ; Plambeck and Siegel, J Combin Theory Ser A, 115: 593–622, 2008 ). The methods are based on the theory of short rational generating functions (Barvinok and Woods, J Am Math Soc, 16: 957–979, 2003 ). Copyright Springer-Verlag 2013

Keywords: Combinatorial game; Lattice game; Convex polyhedron; Generating function; Affine semigroup; Misère quotient (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00182-012-0319-9

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