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Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case

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  • Garratt, Rod

    (U of California, Santa Barbara)

  • Keister, Todd

    (Instituto Tecnologico Autonomo de Mexico)

  • Shell, Karl

    (Cornell U)

Abstract

Sunspot equilibrium and lottery equilibrium are two stochastic solution concepts for nonstochastic economies. Recent work by Garratt, Keister, Qin, and Shell (in press) and Kehoe, Levine, and Prescott (in press) on nonconvex exchange economies has shown that when the randomizing device is continuous, applying the two concepts to the same fundamental economy yields the same set of equilibrium allocations. In the present paper, we examine economies based on a discrete randomizing device. We extend the lottery model so that it can constrain the randomization possibilities available to agents in the same way that the sunspots model can. Every equilibrium allocation of our generalized lottery model has a corresponding sunspot equilibrium allocation. For almost all discrete randomizing devices, the converse is also true. There are exceptions, however: for some randomizing devices, there exist sunspot equilibrium allocations with no lottery equilibrium counterpart.

Suggested Citation

  • Garratt, Rod & Keister, Todd & Shell, Karl, 2002. "Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case," Working Papers 02-07, Cornell University, Center for Analytic Economics.
    • Handle: RePEc:ecl:corcae:02-07
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    References listed on IDEAS

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    1. Rogerson, Richard, 1988. "Indivisible labor, lotteries and equilibrium," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 3-16, January.
    2. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    3. Edward Simpson Prescott & Robert M. Townsend, 2006. "Firms as Clubs in Walrasian Markets with Private Information," Journal of Political Economy, University of Chicago Press, vol. 114(4), pages 644-671, August.
    4. Berentsen, Aleksander & Molico, Miguel & Wright, Randall, 2002. "Indivisibilities, Lotteries, and Monetary Exchange," Journal of Economic Theory, Elsevier, vol. 107(1), pages 70-94, November.
    5. 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.
    6. Shell, Karl & Wright, Randall, 1993. "Indivisibilities, Lotteries, and Sunspot Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-17, January.
    7. Karl Shell & Aditya Goenka, 1997. "Robustness of sunspot equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 79-98.
    8. 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.
    9. Balasko, Yves, 1983. "Extrinsic uncertainty revisited," Journal of Economic Theory, Elsevier, vol. 31(2), pages 203-210, December.
    10. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 295-313, March.
    11. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
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    Cited by:

    1. Prescott, Edward C. & Shell, Karl, 2002. "Introduction to Sunspots and Lotteries," Journal of Economic Theory, Elsevier, vol. 107(1), pages 1-10, November.
    2. Guillaume Rocheteau & Peter Rupert & Randall Wright, 2007. "Inflation and Unemployment in General Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(4), pages 837-855, December.
    3. Guillaume Rocheteau & Peter Rupert & Karl Shell & Randall Wright, 2005. "General equilibrium with nonconvexities, sunspots, and money," Working Papers (Old Series) 0513, Federal Reserve Bank of Cleveland.
    4. Ma, Jinpeng & Nie, Fusheng, 2003. "Walrasian equilibrium in an exchange economy with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 159-192, October.
    5. Rocheteau, Guillaume & Rupert, Peter & Shell, Karl & Wright, Randall, 2008. "General equilibrium with nonconvexities and money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 294-317, September.
    6. Hoelle, Matthew, 2014. "The relation between sunspot effects and multiplicity in incomplete markets models with numeraire assets," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 119-127.
    7. Kokonas, Nikolaos & Monteiro, Paulo Santos, 2021. "Aggregation in economies with search frictions," Journal of Mathematical Economics, Elsevier, vol. 96(C).

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