Double implementation of Lindahl allocations by a pure mechanism

Abstract

This paper considers the issue of designing mechanisms whose Nash allocations and strong Nash allocations coincide with Lindahl allocations for public goods economies when coalition patterns, preferences, and endowments are unknown to the designer. It will be noted that the mechanism presented here is feasible and continuous, and the implementation result is obtained without de®ning an arti®cial preference pro®le on prices announced by individuals. In addition, unlike most existing Nash-implementing mechanisms which need to distinguish the case of two agents from that of three or more agents, this paper provides a uni®ed mechanism which is irrespective of the number of agents.

A solution to the problem of consumption externalities

“…Since the Walrasian mechanism, in general, is not incentive-compatible even for classical economic environments when the number of agents is finite, many incentive-compatible mechanisms have been proposed to implement Walrasian allocations at Nash equilibrium and/or strong Nash equilibrium points such as those in Hurwicz (1979), Schmeidler (1980), Hurwicz et al (1995), Postlewaite and Wettstein (1989), Tian (1992Tian ( , 1999Tian ( , 2000a, Hong (1995), and Peleg (1996a,b) among others.…”

“…Suh (1997) further provided a necessary and sufficient condition for a social choice correspondence to be doubly implementable in Nash and strong Nash equilibrium for a class of economic environments. Many specific mechanisms with a certain desired properties have been proposed to implement some well-known social choice correspondences such as Walrasian allocation, Lindahl allocations, proportional allocations in the literature such as those in Suh (1995), Peleg (1996a,b), Tian (1999, 2000a,b,c), and Yoshihara (1999. Yamato (1993) also considered double implementation in Nash and un-dominated Nash equilibria.…”