A Characterization of Robust Sunspot Equilibria

Abstract

In nonconvex environments, a sunspot equilibrium can sometimes be destroyed by the introduction of new extrinsic information. We provide a simple test for determining whether or not a particular equilibrium survives, or is robust to, all possible re…nements of the state space. We use this test to provide a characterization of the set of robust sunspot-equilibrium allocations of a given economy: it is equivalent to the set of equilibrium allocations of the associated lottery economy. ¤ We thank Huberto Ennis, Aditya Goenka, the associate editor and a referee for providing useful comments. We especially thank Karl Shell for helpful comments and advice.

Growth in economies with non convexities: sunspots and lottery equilibria

“…2 However, when the extrinsic uncertainty space is ([0, 1), B, L), under fairly general assumptions, every sunspot equilibrium allocation induces an equilibrium lottery allocation. If equilibrium allocations of the lottery economy are supported by linear prices, the viceversa is also true, ( [5] and [6]). This equivalence result is based on the assumed existence of sunspot equilibria and, equivalently, of lottery equilibria supported by linear prices.…”

“…The existence of multiple sunspot equilibria provides the rationale for the search of ways to refine sunspot equilibria. ( [7,6]). …”

Comparing Sunspot Equilibrium And Lottery Equilibrium Allocations: The Finite Case*

“…In addition to its theoretical importance, the equivalence result has practical implications, as problems that are difficult to solve in one model may be more easily addressed in the other. For example, Garratt and Keister (2002) show how an outstanding question regarding when sunspot equilibria are robust to refinements in the randomizing device is more easily solved by looking at the lottery formulation of the problem. In addition, when the consumption set has a finite number of elements, finding lottery equilibria reduces to solving a collection of linear programming problems, which can be computationally easier than solving the (nonlinear) sunspots model.…”

Introduction to Sunspots and Lotteries

“…11 In fact, some SE based on a finite sunspot device do not survive refinement of the state space to (finer) finite partitions. The question of whether SE are robust to all refinements of the state space (finite or continuous) is studied in Goenka and Shell [16] and Garratt and Keister [13]. See Antinolfi and Keister [3] for a related notion called strong sunspot immunity.…”

“…Even when there is equivalence of allocations, it is worthwhile to retain both equilibrium concepts: each has its own strengths. For example, Garratt and Keister [13] show how an open question regarding the robustness of sunspot equilibria is easily solved by looking at the lottery formulation of the problem. The SE approach is based on the familiar contingent-commodities approach, and as such is easily applied to a wide variety of settings.…”