NDLI: Algorithms for lattice games

Content Provider	Springer Nature Link
Author	Guo, Alan Miller, Ezra
Copyright Year	2012
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).
Starting Page	777
Ending Page	788
Page Count	12
File Format	PDF
ISSN	00207276
Journal	International Journal of Game Theory
Volume Number	42
Issue Number	4
e-ISSN	14321270
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-01-26
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Combinatorial game Lattice game Convex polyhedron Generating function Affine semigroup Misère quotient Economic Theory Game Theory, Economics, Social and Behav. Sciences Operations Research/Decision Theory Game Theory/Mathematical Methods
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Social Sciences Economics and Econometrics Statistics, Probability and Uncertainty

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