Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
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Alexander M. Chudnov
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.
Originally published in Diskretnaya Matematika (2016) 28, №3, 145–159 (in Russian).
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© 2017 Walter de Gruyter GmbH Berlin/Boston
Articles in the same Issue
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
Articles in the same Issue
- Frontmatter
- Estimating the level of affinity of a quadratic form
- Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
- Large deviations of branching processes with immigration in random environment
- On the probability of existence of substrings with the same structure in a random sequence
- Linearly realizable automata
- On the number of labeled outerplanar k-cycle blocks
- Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
