On the probability of breakdown in participation games
分析了一种参与博弈（公共品博弈的变体），其中个人贡献是二元的（参与或不参与）。不同于以往研究假设公共品收益与贡献人数无关，本文放松了这一假设，证明了崩溃概率（无人参与的概率）随群体规模变化的条件，并发现大群体中该概率在极限下不可忽略，预期参与者数小于1。
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.