Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games

A. M. Chudnov

S. M. Budyonny Military Academy of Communications

Abstract: We study conditions for the existence of coalition games with the result invariant under cyclic shifts of players sequence numbers. Given a total number $ n $ of players, we estimate the number $ k $ of players of one coalition under which there exists a game in which this coalition wins under all cyclic shifts of players. We give procedures for construction of the so-called set-splitting digraphs on which risk-free nim-type games of a given coalition are defined.

Keywords: positional game, risk-free game, cyclic sequence, difference set.

UDC: 519.833.5+519.172.3+519.116

Received: 04.04.2016
Revised: 11.08.2016

DOI: 10.4213/dm1388

 English version: Discrete Mathematics and Applications, 2017, 27:6, 349–359

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