Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting

The purpose of this paper is to show how conjectural variations can be derived as a reduced form in an infinitely repeated game of private provision of public goods. We obtain explicit closed forms of conjectural variations associated with maximal sustainable equilibria in which the sum of the utilities of all of a community's members is maximized for both quadratic and Cobb–Douglas preferences, provided that the resulting sequence of contributions can be sustained as a Nash (or subgame perfect) equilibrium in the underlying repeated game. We also show that positive conjectural variations will emerge as long as people place positive weight on the future, and that those conjectures are positively related to the discount factor.