  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.
