Nash implementation with a private good

Abstract

I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Copyright Springer-Verlag Berlin Heidelberg 2003Keywords and Phrases: Nash implementation, Lindahl equilibrium, Walrasian equilibrium, Simple mechanisms., JEL Classification Numbers: D78.,

Implementation of Pareto efficient allocations

“…The most commonly used equilibrium principles that result in Pareto optimal allocations are the Walrasian equilibrium, proportional equilibrium and Lindahl distributive equilibrium solutions for private goods economies, Lindahl equilibrium, ratio equilibrium and cost share equilibrium solutions for public goods economies. Many specific mechanisms have been provided in the literature that implement theseequilibrium principles such as those in Hurwicz (1979); Schmeidler (1980); Hurwicz et al (1995); Postlewaite and Wettstein (1989); Tian (1989Tian ( , 1994Tian ( , 1996Tian ( , 2003; Hong (1995); Peleg (1996a, b); Suh (1995Suh ( , 1997; Yoshihara (1999); Duggan (2003) among others. The implementation literature rarely discusses implementation of the whole set of Pareto efficient allocations under private ownership or more generally under other ownership structures.…”

Implementation of marginal cost pricing equilibrium allocations with transfers in economies with increasing returns to scale

“…Until recently, most studies have been largely devoted to pure exchange models or economies with convex production possibility sets such as those in Hurwicz (1979), Schmeidler (1980), Hurwicz, Maskin, and Postlewaite (1995), Postlewaite and Wettstein (1989), Tian (1989Tian ( , 1992Tian ( , 1996Tian ( , 1999, Hong (1995), and Peleg (1996), Suh (1995), Yoshihara, (1999), Duggan (2003), among others. Recently, Tian (2009a) considered the problem of the incentive mechanism design for economies with non-convexities in production technologies.…”

Implementation in economies with non-convex production technologies unknown to the designer

“…Like most characterization results in the literature, Hurwicz-Maskin-Postlewaite's mechanism is not continuous. The "better" mechanism design, which requires some desired properties such as continuity, feasibility, and lower dimensionality, has mainly been done only for exchange economies or convex production economies such as those in Groves and Ledyard (1977), Hurwicz (1979), Schmeidler (1980), Hurwicz et al (1995), Postlewaite and Wettstein (1989), Tian (1989Tian ( , 1992aTian ( , 1992bTian ( , 1996Tian ( , 1999, Hong (1995), Peleg (1996), and Duggan (2003), among others. Tian (2005) considered this mechanism design for non-convex production economies.…”