Comparing Sunspot Equilibrium and Lottery Equilibrium Allocations: The Finite Case

Sunspot equilibrium and lottery equilibrium are two stochastic solution concepts for nonstochastic economies. Recent work on nonconvex exchange economies has shown that when the randomizing device is a continuous random variable, 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, which corresponds to the case where there is only a finite number of sunspot states. 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 constrained lottery model has a corresponding sunspot equilibrium allocation. For almost all finite 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. * We thank Bob Anderson, Jess Benhabib, Alberto Bisin, Luca Bossi, David Easley, Richard Rogerson, Manuel Santos, Neil Wallace, Randy Wright, two anonymous referees, and especially Jim Peck for helpful comments and discussions. We also thank seminar participants at Arizona State, Cornell, the Federal Reserve Bank of Cleveland, ITAM, Ohio State, Stanford, Universitat Autònoma de Barcelona, UCSD, Washington University, the NBER General Equilibrium Conference, the Extrinsic Uncertainty Workshop at NYU, the Cornell/Penn State Macroeconomics Workshop, and the Meetings of the Society for the Advancement of Economic Theory. Part of this work was completed while Keister was visiting the University of Texas at Austin, whose hospitality and support are gratefully acknowledged.