Repeated Public Good Provision

We provide a tractable framework for studying the e¤ects of group size and structure on the maximum level of a public good that can be provided in sequential equilibrium in repeated games with private monitoring. We restrict attention to games with "all-or-nothing" monitoring, in which in every period player i either perfectly observes player j’s contribution to the public good or gets no information about player j’s contribution; this class of games includes many interesting examples, including random matching, monitoring on networks, and simple kinds of imperfect "quasi-public" monitoring. The …rst main result is that the maximum level of public good provision can be sustained in grim trigger strategies. In games satisfying a weak form of symmetry, comparative statics on the maximum per capita level of public good provision are shown to depend only on the product of a term capturing the rivalness of the good and a term capturing a simple characteristic of the monitoring technology: its "e¤ective contagiousness." In leading examples, the maximum per capita level of provision of a pure public good is increasing in group size, but the maximum per capita level of provision of a divisible public good is often decreasing in group size. Under broad conditions, making monitoring less uncertain in the second-order stochastic dominance sense increases public good provision. For games played on asymmetric networks, we introduce a new notion of network centrality and show that more central players in social networks make larger contributions, and that every player in better connected networks can contribute more to the public good. We also consider an extension to local public goods. I thank Daron Acemoglu, Glenn Ellison, and Muhamet Yildiz for detailed comments and suggestions and for extensive advice and support; and thank Abhijit Banerjee, Alessandro Bonatti, Gabriel Carroll, Anton Kolotilin, Parag Pathak, and Iván Werning for helpful comments and discussions. I thank the NSF for …nancial support.