Production Targets and Free Disposal in the Private Provision of Public Goods

In a collective-action game a player`s payoff is the sum of (i) a private component that depends only on that player`s action, and (ii) a public component, common to all players and dependent upon all actions. A classic application is the private provision of a public good. Play evolves: strategy revisions are made according to a multinomial-logit choice rule. Long-run behaviour is determined by a potential function, which incorporates the private (not social) benefits of activity. Behaviour may be influenced only by reducing public-good output (an application of a free-disposal property). When welfare is the expected time average of aggregate payoffs, it is socially optimal to either leave production well alone, or damage it as much as possible. This often takes the form of a production target, where all output is discarded unless some threshold is reached, potentially generating an equilibrium-selection problem. When the evolution of play approximates a best-reply process, the optimal threshold corresponds to the output level that an individual who pays all private costs but enjoys only private benefits would be just willing to provide.