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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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Suggested Citation

  • Rod Garratt, 2010. "Decentralizing Lottery Allocations in Markets With Indivisible Commodities," Levine's Working Paper Archive 2087, David K. Levine.
    • Handle: RePEc:cla:levarc:2087
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    Cited by:

    1. Koshevoy, Gleb A. & Talman, Dolf, 2006. "Competitive equilibria in economies with multiple indivisible and multiple divisible commodities," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 216-226, April.
    2. 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, vol. 103(2), pages 411-428, April.
    3. Alberto Bennardo & Salvatore Piccolo, 2014. "Competitive Markets With Endogenous Health Risks," Journal of the European Economic Association, European Economic Association, vol. 12(3), pages 755-790, June.
    4. Kehoe, Timothy J. & Levine, David K. & Prescott, Edward C., 2002. "Lotteries, Sunspots, and Incentive Constraints," Journal of Economic Theory, Elsevier, vol. 107(1), pages 39-69, November.
    5. Ma, Jinpeng & Nie, Fusheng, 2003. "Walrasian equilibrium in an exchange economy with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 159-192, October.
    6. Kokonas, Nikolaos & Monteiro, Paulo Santos, 2021. "Aggregation in economies with search frictions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    7. van der Laan, G. & 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," Other publications TiSEM 5a5610bf-4f85-4a25-963c-c, Tilburg University, School of Economics and Management.
    8. Garratt, Rod & Keister, Todd & Qin, Cheng-Zhong & Shell, Karl, 2002. "Equilibrium Prices When the Sunspot Variable Is Continuous," Journal of Economic Theory, Elsevier, vol. 107(1), pages 11-38, November.
    9. Prescott, Edward C. & Shell, Karl, 2002. "Introduction to Sunspots and Lotteries," Journal of Economic Theory, Elsevier, vol. 107(1), pages 1-10, November.
    10. Peck, James, 1996. "Competition in Transactions Mechanisms: The Emergence of Price Competition," Games and Economic Behavior, Elsevier, vol. 16(1), pages 109-123, September.
    11. Rod Garratt & Todd Keister & Karl Shell, 2004. "Comparing Sunspot Equilibrium And Lottery Equilibrium Allocations: The Finite Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 351-386, May.
    12. Camelia Bejan & Juan Camilo Gómez, 2017. "Employment lotteries, endogenous firm formation and the aspiration core," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 215-226, October.
    13. repec:cdl:ucsbec:12-99 is not listed on IDEAS
    14. Garratt, Rod & Keister, Todd, 2002. "A Characterization of Robust Sunspot Equilibria," Journal of Economic Theory, Elsevier, vol. 107(1), pages 136-144, November.
    15. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Discussion Paper 2006-51, Tilburg University, Center for Economic Research.
    16. Alberto Bennardo & Salvatore Piccolo, 2005. "Competitive occupational choices with endogenous health risks," Levine's Working Paper Archive 784828000000000199, David K. Levine.
    17. Rocheteau, Guillaume & Wang, Lu, 2023. "Endogenous liquidity and volatility," Journal of Economic Theory, Elsevier, vol. 210(C).
    18. repec:fth:calaec:12-99 is not listed on IDEAS
    19. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    20. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, vol. 77(1), pages 81-101, November.

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