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Decentralizing Lottery Allocations in Markets With Indivisible Commodities

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  • Rod Garratt

Abstract

In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisfying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev. 25, 1-20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common "sunspot device" as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ. 91, 193-227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 2087.

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Date of creation: 09 Dec 2010
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Handle: RePEc:cla:levarc:2087

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Cited by:
  1. Garratt, Rod & Keister, Todd & Shell, Karl, 2002. "Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case," Working Papers, Cornell University, Center for Analytic Economics 02-07, Cornell University, Center for Analytic Economics.
  2. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Discussion Paper, Tilburg University, Center for Economic Research 2006-51, Tilburg University, Center for Economic Research.
  3. James Peck, 1995. "Competition in Transactions Mechanisms: The Emergence of Price Competition," Working Papers, Ohio State University, Department of Economics 022, Ohio State University, Department of Economics.
  4. Ma, Jinpeng & Nie, Fusheng, 2003. "Walrasian equilibrium in an exchange economy with indivisibilities," Mathematical Social Sciences, Elsevier, Elsevier, vol. 46(2), pages 159-192, October.
  5. Alberto Bennardo & Salvatore Piccolo, 2005. "Competitive Markets with Endogenous Health Risks," CSEF Working Papers, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy 145, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Mar 2008.
  6. Koshevoy, G.A. & Talman, A.J.J., 2002. "Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities," Discussion Paper, Tilburg University, Center for Economic Research 2002-71, Tilburg University, Center for Economic Research.
  7. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2002. "Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production," Open Access publications from Tilburg University urn:nbn:nl:ui:12-89376, Tilburg University.
  8. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 81-101, November.
  9. repec:fth:calaec:12-99 is not listed on IDEAS
  10. Prescott, Edward C. & Shell, Karl, 2002. "Introduction to Sunspots and Lotteries," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(1), pages 1-10, November.
  11. Garratt, Rod & Keister, Todd, 2002. "A Characterization of Robust Sunspot Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(1), pages 136-144, November.
  12. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, Elsevier, vol. 103(2), pages 411-428, April.
  13. Garratt, Rod & Keister, Todd & Qin, Cheng-Zhong & Shell, Karl, 2002. "Equilibrium Prices When the Sunspot Variable Is Continuous," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(1), pages 11-38, November.
  14. Alberto Bennardo & Salvatore Piccolo, 2005. "Competitive occupational choices with endogenous health risks," Levine's Working Paper Archive 784828000000000199, David K. Levine.
  15. Timothy J. Kehoe & David K. Levine & Edward Prescott, 2000. "Lotteries, Sunspots and Incentive Constraints," Levine's Working Paper Archive 1974, David K. Levine.

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