European Journal of Political Economy 7 (1991) 55-64. North-Holland Implementing the Lindahl voluntary-exchange mechanism Leif Danziger* Bar-Ilan University, Ramat Gan 52900, Israel, and York University, Toronto, Ontario M3J IP3, Canada Adi Schnytzer Bar-llan University, Ramat Gan 52900, Israel Accepted for publication December 1990 This paper analyzes a two-stage game for implementing Lindahl’s voluntary-exchange mecha- nism. The game is based on a model of matching behavior suggested by Guttman (1978). Both the price and the quantities purchased of the public good are individualized, and Lindahl prices emerge endogenously in the lirst stage of the game. It is shown that any perfect equilibrium with a positive provision of the public good is a Lindahl equilibrium. There might also exist non- provision perfect equilibria that are Pareto dominated by Lindahl equilibria with positive provision of the public good. 1. Introduction Lindahl’s classic voluntary-exchange mechanism for the provision of pure public goods [Lindahl (1919/1967)] is based on the assumption that contributions are the outcome of ‘free agreement’, in the same manner as the acquisition of private goods in a free market. As presented by Lindahl, however, the voluntary-exchange mechanism relies on ill-defined notions of ‘equal bargaining power’ and ‘exchange up to saturation’, and Lindahl chose a particular Pareto optimal outcome without demonstrating that it is attainable as an equilibrium in any competitive process.’ In this paper we analyze a two-stage game for implementing Lindahl’s voluntary-exchange mechanism. The game is based on the model of matching behavior proposed by Guttman (1978,1985,1987). In the Lindahl- implementing game - as we shall call it - Lindahl prices and Pareto optimal *The author is grateful to the Research Group for the Public Sector at the University of Copenhagen for their hospitality. ‘In fact, Lindahl himself (albeit serendipitously) pointed out that the chosen outcome cannot be a equilibrium since ‘at this point one party could still improve distribution from its point of view by restricting demand’ [Lindahl (1919/1967, p. 172)]. 01762680/91/603.50 0 1991-Elsevier Science Publishers B.V. (North-Holland)