Cores and competitive equilibria with indivisibilities and lotteries

Lotteries are introduced in the exchange model of Shapley and Scarf (J. Math. Econ. 1 (1974), 23-37). In competition, traders buy and sell probabilities on houses. When considering the core, feasible allocations of the economy and blocking allocations of coalitions may involve lotteries. Among other results, we show that the set of lottery equilibrium allocations is non-empty and does not contain all competitive equilibrium allocations, the core of the Shapley/Scarf model is a strict subset of the lottery core, and lottery equilibrium allocations are contained in the lottery core. (C) 1996 Academic Press, Inc.