Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium.

[1]  Randomization with Asymmetric Information a Simplified Exposition , 1985 .

[2]  Fernando Alvarez,et al.  Asset Pricing When Risk Sharing is Limited by Default , 1997 .

[3]  Richard Rogerson,et al.  Indivisible labor, lotteries and equilibrium , 1988 .

[4]  D. Levine,et al.  Liquidity Constrained Markets Versus Debt Constrained Markets , 2001 .

[5]  Narayana R. Kocherlakota,et al.  Efficient Allocations with Hidden Income and Hidden Storage , 2001 .

[6]  Dirk Krueger.  Risk Sharing in Economies with Incomplete Markets , 1999 .

[7]  P. Gottardi,et al.  Competitive Equilibria with Asymmetric Information , 1999 .

[8]  John Geanakoplos,et al.  An introduction to general equilibrium with incomplete asset markets , 1990 .

[9]  Edward C. Prescott,et al.  Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard , 1984 .

[10]  John C. Fellingham,et al.  Ex ante randomization in agency models , 1984 .

[11]  Karl Shell,et al.  Equilibrium Prices When the Sunspot Variable Is Continuous , 2002, J. Econ. Theory.

[12]  Fernando Alvarez,et al.  Efficiency, equilibrium, and asset pricing with risk of default , 2000 .

[13]  David K. Levine,et al.  Debt-Constrained Asset Markets , 1993 .

[14]  Richard T. Boylan.  Laws of large numbers for dynamical systems with randomly matched individuals , 1992 .

[15]  G. Hansen.  Indivisible Labor and the Business Cycle , 1985 .

[16]  Randall Wright,et al.  Indivisibilities, lotteries, and sunspot equilibria , 1993 .

[17]  Rodney Garratt,et al.  Decentralizing lottery allocations in markets with indivisible commodities , 1995 .

[18]  Harold L. Cole,et al.  Valuation Equilibrium with Clubs , 1997 .

[19]  Enrico Tronci.  1997 , 1997, Les 25 ans de l’OMC: Une rétrospective en photos.

[20]  Frøystein Gjesdal,et al.  Information and Incentives: The Agency Information Problem , 1982 .

[21]  Bengt Holmstrom,et al.  Moral Hazard and Observability , 1979 .

[22]  Robert M. Townsend,et al.  Firms as Clubs in Walrasian Markets with Private Information , 2000 .

[23]  N. Kocherlakota.  Implications of Efficient Risk Sharing Without Commitment , 1996 .

[24]  Harold L. Cole.  Comment: General competitive Analysis in an Economy with Private Information , 1989 .

[25]  H. Uhlig.  A law of large numbers for large economies , 1996 .

[26]  Harold L. Cole,et al.  Valuation equilibria with clubs , 1996 .

[27]  Edward C. Prescott,et al.  General Competitive Analysis in an Economy with Private Information , 1984 .