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 previous work 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 and exceeding e−1 in the limit and that the expected number of participants is
less than one. Also two economic examples, concerning R&D and debt overhang, are discussed.