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 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.