Double implementation of linear cost share equilibrium allocations

Abstract

In this paper we consider the problem of double implementation of Linear Cost Share Equilibrium (LCSE) allocations by a feasible and continuous mechanism whose Nash allocations and strong Nash allocations coincide with Linear Cost Share Equilibrium allocations. The mechanism presented here allows preferences and initial endowments as well as coalition patterns to be privately observed, a feature missing from much recent work in implementation theory. Since LCSE contains Lindahl equilibrium and Ratio equilibrium as special cases, it doubly implements these two equilibria allocations. Further, if one reinterprets the commodity space, this mechanism also doubly implements Walrasian allocations for private goods economies. Thus, the mechanism given in the paper appears to represent a ‘generic’ mechanism to doubly implement market-type allocations in private and/or public goods economies.