Decentralizing Lottery Allocations in Markets with Indivisible Commodities.

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.