Nimbers are inevitable

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چکیده

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Nimbers are inevitable

This article concerns the resolution of impartial combinatorial games, and in particular games that can be split in sums of independent positions. We prove that in order to compute the outcome of a sum of independent positions, it is always more efficient to compute separately the nimbers of each independent position than to develop directly the game tree of the sum. The concept of nimber is th...

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Recessions and other crises seem to occur without any large exogenous shocks. One theory is that this is due to strategic complementarities: the incentive to invest is stronger if others are expected to invest. If, in addition, each investor observes a slightly noisy signal of the true fundamentals, a crisis occurs whenever fundamentals fall below a certain threshold (Morris and Shin, AER 1998)...

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Kayles and Nimbers

Kayles is a combinatorial game on graphs. Two players select alternatingly a vertex from a given graph G a chosen vertex may not be adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. The problem to determine which player has a winning strategy is known to be PSPACE-complete. Because of certain characteristics of the Kayles game, it can be anal...

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ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2012

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2012.09.002