"Club good mechanisms : from free-riders to citizen-shareholders, from impossibility to characterization"

joint work with Christian Trudeau

Paper attached.

Abstract.
Consider a community that shares a technology for producing a club good (Buchanan, 1965) : any group of agents can "win" for an associated monetary cost. Who should win, and how should production be funded ? To address this question, we seek rules (that is, direct mechanisms) where each agent participates voluntarily and is incentivized to report his valuation honestly, and where these reports are used to select winners efficiently without running a deficit.
We find that whether or not there are such rules depends on the production technology. If costs are even "somewhat concave," then there are no such rules : the free-rider problem (Wicksell, 1896 ; Samuelson, 1954 ; Green and Laffont, 1979) persists even when agents who do not contribute can be excluded. If costs are symmetric and convex, however, then there are such rules that moreover satisfy no-envy-in-trades (Kolm, 1971 ; Schmeidler and Vind, 1972). We characterize this class, whose Pareto-worst member is the familiar minimum-price Walrasian rule (Vickrey, 1961 ; Clarke, 1971 ; Groves, 1973 ; Demange, 1982 ; Leonard, 1983) ; the other rules do better by treating the agents as equal shareholders in the technology and offering social dividends (Lange, 1936).