In this paper we examine the competitive equilibria of a dynamic stochastic economywith complete markets. We show that the completeness of the market requires both theset of asset payo¤s and collateral levels to be su¢ ciently rich, so as to allow to decentral-ize the equilibrium allocations obtained in Arrow-Debreu markets subject to a series ofappropriate limited pledgeability constraints. We provide then su¢ cient conditions forequilibria to be Pareto e¢ cient and show that when collateral is scarce equilibria are alsooften constrained ine¢ cient, in the sense that imposing tighter borrowing restrictionscan make everybody in the economy better o¤.We derive su¢ cient conditions for the existence of Markov equilibria and show thatthey often have ?nite support. The model is then tractable and its equilibria can becomputed with arbitrary accuracy. We carry out on this basis a quantitative assessmentof the risk sharing and e¢ ciency properties of equilibria.