Computability of simple games: A characterization and application to the core

Details Computability of simple games: A characterization and application to the core Computability of simple games: A characterization and application to the core

2007-05-22

arxiv.org/abs/0705.3227v2

Journal of Mathematical Economics, Volume 44, Issues 3-4, February 2008, Pages 348-366

Computer Science

Computer Science and Game Theory

35 pages; To appear in Journal of Mathematical Economics; Appendix added, Propositions, Remarks, etc. are renumbered

Scientific paper

10.1016/j.jmateco.2007.05.012

The class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura's theorem about the nonemptyness of the core and shows that computable games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted.

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