Double implementation of the Lindahl equilibrium by a continuous mechanism

Abstract

J41, Lindahl equilibrium, Implementation, Nash and strong equilibrium,

A family of supermodular Nash mechanisms implementing Lindahl allocations

“…In particular, some mechanisms have been discovered which have the property that Nash equilibria are Pareto optimal 2 . These can be found in the work of Groves and Ledyard (1977), Hurwicz (1979), Walker (1981), Tian (1989), Kim (1993), Peleg (1996) and Falkinger (1996).…”

Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear

“…We notice that continuous di¤erentiability is just a little bit stronger than continuity because continuous functions can be approximated by di¤erentiable functions, Bartle (1976), p. 172. And continuity is a sensible requirement in mechanism design, Postlewaite and Wettstein (1989) and Peleg (1996). However the di¤erentiable approach eliminates strategy-proof solutions that are not di¤erentiable like the generalized medians and the uniform rule.…”

Double implementation of Lindahl allocations by a pure mechanism

“…Recently, Peleg (1996b) gave a feasible and continuous mechanism with a ®nite dimensional message space, which attempts to doubly implement Lindahl allocations. The main drawback of his mechanism is that the mechanism is not a pure mechanism in the sense that a preference relation is arti®cially introduced for individuals to rank announced prices.…”

“…In Peleg's approach, an individual is not only a player, but also an inside auctioneer. Unlike the usual auctioneer de®ned in the literature, the auctioneers de®ned in Peleg (1996b) not only announce and adjust prices, but are also as assigned preferences on the level of prices announced. In an incentive mechanism design, the preferences of agents should be given, not assigned, since it is private information to the designer.…”

“…Our implementation result is obtained without changing individuals' preferences and thus improves the mechanism proposed in Peleg (1996b) so as to avoid introducing arti®cial preference relations for prices announced by individuals.1 In addition, our mechanism works not only for three or more agents, but also for a two-agent world. While most of the mechanisms mentioned above need to distinguish 1 We also use a weaker assumption that preferences are increasing only in private goods while Peleg (1996b) assumed that preferences are increasing in both private and public goods. the case of two agents from that of three or more agents, this paper gives a uni®ed mechanism which is irrespective of the number of agents.…”