DECENTRALIZING LOTTERY ALLOCATIONS IN MARKETS WITH INDIVISIBLE COMMODITIES

In economies with indivisible commodities, consumers tend to prefer lo tteries in commodities. A potential mechanism for satisfying these pre ferences is unrestricted purchasing and selling of lotteries in decent ralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev . 25, 1-20]. However, this paper shows in several examples that such l ottery 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 boun ded or if lotteries are based upon a common ''sunspot device'' as defi ned by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ. 91, 193-2 27]. The paper shows that any lottery equilibrium is either a Walrasia n equilibrium or a sunspot equilibrium, but there are Walrasian and su nspot equilibria that are not lottery equilibria.