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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
437.
Length: Date of creation: Aug 2007 Date of revision: Publication status: Published in Journal of Mathematical Economics 3-4.44(2008): pp. 348-366 Handle: RePEc:pra:mprapa:437
Find related papers by JEL classification: C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games D90 - Microeconomics - - Intertemporal Choice and Growth - - - General D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other
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