Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.