A Dynamic Conjectural Variations Model in the Private Provision of Public Goods: a Differential Game Approach

The purpose of this paper is to provide reasonable microfoundation to justify the concept of a conjectural valuations equilibrium which is often used in the literature on the private provision of public goods by incorporating an explicit dynamic process of learning with the help of the differential game. By interpreting the steady state conjectures in such a dynamic provision game as the conjectural variations variations in the corresponding static game, we derive zero or nonzero conjectural variations as an outcome of a learning process. Furthermore, we find that there may be uncountable conjectural variations and the possibility of matching behavior (i.e., positive conjectures), when nonlinear feedback strategies are available and when the domain of a state variable is appropriately restricted.