On the probability of breakdown in participation games

In this paper I analyze a participation game i.e. a public good game where
contributions to the public good are binary (people either participate or not participate).
Although variants of this game have been studied extensively, most previouswork takes
the benefit of provision of the public good to be independent of the number of players
that contribute and show that the probability of breakdown, i.e. the probability that
no one participates, is increasing in group size. Here this assumption is dropped. I
show when the probability of breakdown is decreasing in group size and also present
sufficient conditions under which the probability of breakdown is increasing in group
size. Moreover I show that for large groups this probability is non-negligible in the
limit and that the expected number of participants is less than one. Two economic
examples, concerning R&D and debt overhang, are discussed.