When does one bad apple spoil the barrel? An evolutionary analysis of collective action

This paper studies collective-action games in which the production of a public good requires teamwork. A leading example is a threshold game in which provision requires the voluntary participation of m out of n players. Quantal-response strategy revisions allow play to move between equilibria in which a team successfully provides, and an equilibrium in which the collective action fails. A full characterization of long-run play reveals the determinants of success; these include the correlation between players' costs of provision and their valuations for the good. The addition of an extra "bad apple" player can "spoil the barrel" by destabilizing successful teams and so offers a rationale for limiting the pool of possible contributors.