Tian, Guoqiang (1991): Implementation of the Walrasian Correspondence without Continuous, Convex, and Ordered Preferences. Published in: Social Chioce and Welfare , Vol. 9, (1992): pp. 117130.

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Abstract
This paper consideres the problem of designing better mechanisms whose Nash allocations coincide with constrained Walrasian allocations for nonneoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walraisan correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for nonneoclassical economies, there are incentivecompatible, privacy preserving, and wellbehaved mechanisms which yield Paretoefficient and individually rational allocations at Nash equilibria.
Item Type:  MPRA Paper 

Original Title:  Implementation of the Walrasian Correspondence without Continuous, Convex, and Ordered Preferences 
Language:  English 
Keywords:  Walrasian Correspondence; Convex; Ordered Preferences 
Subjects:  D  Microeconomics > D5  General Equilibrium and Disequilibrium 
Item ID:  41298 
Depositing User:  Guoqiang Tian 
Date Deposited:  19. Sep 2012 11:38 
Last Modified:  29. Jul 2015 16:46 
References:  Abreu R, Sen A (1988) Subgame perfect implementation: a necessary and almost sufficient condition. J Econ Theory 50: 285299 Bergson A (1938) A reformulation of certain aspects of welfare economics. Q J Econ 52: 310334 Debreu G (1959) Theory of value. Wiley, New York Groves T, Ledyard J (1977) Optimal allocation of public goods: a solution to the free rider' problem. Econometrica 45: 783811 Groves T, Ledyard J (1987) Incentive compatibility since 1972. In: Groves T, Radner R, Reiter S (eds) Information, incentive, and economic mechanisms. University of Minnesota Press, Minneapolis, MN Hurwicz L (1960) Optimality and informational efficiency in resource allocation processes. In: Arrow KJ, Karlin S, Suppes P (eds) Mathematical methods in the social sciences. Stanford University Press, Stanford Hurwicz L (1972) On informationally decentralized systems. In: Radner R, McGuire CB (eds) Decision and organization, p 297336, (volume in honor of J Marschak). Elsevier, NorthHolland, Amsterdam Hurwicz L (1979a) Outcome functions yielding Walrasian and Lindahl allocations at Nash equilibrium points. Rev Econ Stud 46: 217225 Hurwicz L (1979b) On allocations attainable through Nash equilibria. J Econ Theory 21: 149165 Hurwicz L (1985) A perspective. In: Hurwicz L, Schmediler D, Sonnenschein H (eds) Social goals and social organization — essays in memory of Elisha Pazner, p 116. Cambridge University Press, Cambridge Hurwicz L (1986a) Incentive aspects of decentralization. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics, vol III, p 14411482. Elsevier, NorthHolland, Amsterdam Hurwicz L (1986b) On the implementation of social choice rules in irrational societies. In: Heller WP, Ross RM, Starrett DA (eds) Social choice and public decision making — essays in honor of Kenneth J Arrow, vol I, p 7596. Cambridge University Press, Cambridge Hurwicz L (1986c) On informational decentralization and efficiency in resource allocation mechanism. In: Reiter S (ed) Studies in mathematical economics. Mathematical Association of America Hurwicz L, Maskin E, Postlewaite A (1984) Feasible implementation of social choice correspondences by Nash equilibria. University of Minnesota (mimeo) Kim T, Richter MK (1986) Nontransitivenontotal consumer theory. J Econ Theory 38: 324363 Kwan KY, Nakamura S (1987) On Nash implementation of the Walrasian or Lindahl correspondence in the twoagent economy. Discussion Ppaer #243, University of Minnesota Lange O (1942) The foundation of welfare economics. Econometrica 10: 215228 MasColell A (1974) An equilibrium existence theorem without complete or transitive preferences. J Math Econ 1: 237246 MasColell A (1985) Theory of general economic equilibrium — a differentiable approach. Cambridge University Press, Cambridge Maskin E (1977) Nash equilibrium and welfare optimality. M.I.T., October (mimeo) Moore J, Repullo R (1988) Subgame game perfect implementation. Econometrica 56: 11911220 Mosteller F, Nogee P (1951) An experimental measure of utility. J Polit Econ 59: 371404 Palfrey T, Srivastava S (1991) Nash implementation using undominated strategy. Econometrica 59: 479502 Postlewaite A, Wettstein D (1983) Implementing constrained Walrasian equilibria continuously. CARESS Discussion Paper 8324,University of Pennsylvania, Philadelphia Postlewaite A, Wettstein D (1989) Continuous and feasible implementation. Rev Econ Stud 56: 603611 Schmeidler D (1969) Competitive equilibrium in markets with a continuum of traders and incomplete preferences. Econometrica 37: 578585 Schmeidler D (1980) Walrasian analysis via strategic outcome functions. Econometrica 48: 15851593 Shafer W, Sonnenschein H (1975) Equilibrium in abstract economies without ordered preferences. J Math Econ 2: 345348 Sonneschein H (1971) Demand theory without transitive preferences, with application to theory of competitive equilibrium. In: Chipman, JS, Hurwicz L, Richter MK, Sonnenschein H (eds) Preferences, utility, and demand. Harcourt Brace Jovanovich, New York Thomson W (1985) Manipulation and implementation in economics. University of Rochester, unpublished book Tian G (1987) Nashimplementation of social choice correspondences by completely feasible continuous outcome functions. Ph. D. Dissertation, University of Minnesota Tian G (1988) On the constrained Walrasian and Lindahl correspondences. Econ Lett 26: 299303 Tian G (1989) Implementation of the Lindahl correspondence by a singlevalued, feasible, and continuous mechanism. Rev Econ Stud 56: 613621 Tian G (1990) Completely feasible and continuous Nashimplementation of the Lindahl correspondence with a message space of minimal dimension. J Econ Theory 51: 443452 Tian G (1991a) Fixed points theorems for mappings with noncompact and nonconvex domains. J Math Anal Appl 158: 161167 Tian G (1991b) Implementation of Lindahl allocations with nontotalnontransitive preferences. J Publ Econ 46: 247259 Tian G (1992) Generalizations of the FKKM theorem and KyFan minimax inequality. with applications to maximal elements, price equilibrium, and complementarity. J Math Anal Appl (forthcoming papers) Tian G, Li Q (1991) Completely feasible and continuous implementation of the Lindahl correspondence with any number of goods. Math Soc Sci 21: 6779 Tian G, Zhou, J (1991) Quasivariational inequalities with noncompact sets. J Math Anal Appl 160: 583595 Walker (1981) A simple incentive compatible scheme for attaining Lindahl allocations. Econometrica 49: 6571 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/41298 