Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. When these consumers trade in a sequence of markets, their time-inconsistency may introduce a non-convexity that gives them an incentive to trade lotteries. If there are many consumers, competitive equilibria with and without lotteries exist. The existence of symmetric equilibria may require lotteries. Symmetric equilibria that do not require lotteries are generically locally unique. Allocations that are Pareto efficient at the initial date are also renegotiation-proof. Competitive equilibria are Pareto efficient in this sense, and for generic endowments, if and only if preferences are locally homothetic. For non-homothetic preferences, the introduction of lottery markets has an ambiguous impact on the equilibrium welfare of consumers at the initial date.