A characterization of natural and double implementation in production economies

Abstract. We define two types of natural mechanisms, quantity and price-quantity types, in convex production economies, and characterize the class of Pareto subsolutions doubly implementable in Nash and strong Nash equilibria by these mechanisms respectively. First, we show that there is a class of Pareto subsolutions doubly implementable by natural quantity mechanisms, as long as production sets have smooth boundaries. We characterize the class of Pareto subsolutions doubly implementable by natural price-quantity mechanisms without assuming differentiability of utility functions. Third, we show that the Walrasian solution is the unique Pareto and fully individually rational solution naturally and doubly implementable in private ownership economies.

[1]  Matthew O. Jackson,et al.  Undominated Nash Implementation in Bounded Mechanisms , 1994 .

[2]  Sang-Chul Suh,et al.  Double Implementation by a Simple Game Form in the Commons Problem , 1997 .

[3]  David Schmeidler,et al.  Walrasian Analysis via Strategic Outcome Functions , 1980 .

[4]  Guoqiang Tian.  Incentive Mechanism Design for Production Economies with Both Private and Public Ownerships , 2000, Games Econ. Behav..

[5]  Sang-Chul Suh,et al.  A characterization of the Walras rule , 1995 .

[6]  Naoki Yoshihara.  Natural and double implementation of public ownership solutions in differentiable production economies , 1999 .

[7]  J. Roemer,et al.  The Proportional Solution for Economies with Both Private and Public Ownership , 1993 .

[8]  Andrew Postlewaite,et al.  Feasible Nash Implementation of Social Choice Rules When the Designer Does not Know Endowments or Production Sets , 1995 .

[9]  Tatsuyoshi Saijo,et al.  Toward Natural Implementation , 1996 .

[10]  Tomas Sjöström,et al.  Implementation by demand mechanisms , 1994 .

[11]  Double implementation in Nash and strong Nash equilibria , 1997 .

[12]  Arunava Sen,et al.  Nash implementation through elementary mechanisms in economic environments , 1994 .

[13]  T. Saijo,et al.  Characterizing Natural Implementability: The Fair and Walrasian Correspondences , 1999 .

[14]  Lu Hong.  Nash implementation in production economies , 1995 .

[15]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[16]  Leonid Hurwicz,et al.  On allocations attainable through Nash equilibria , 1979 .

[17]  L. Hurwicz.  Studies in Resource Allocation Processes: Optimality and informational efficiency in resource allocation processes , 1977 .