Feasible Mechanisms in Economies with Type-Dependent Endowments

We consider N.T.U. and T.U. exchange economies in which initial endowments and preferences depend on the agents’private information. Every agent knows his own initial endowment, but his utility over consumption bundles possibly depends on the others’information (common values). We describe general allocation games in which agents make non-veri…able claims about their types and e¤ective deposits of consumption goods. The planner redistributes the goods that are deposited by the agents. In W-allocation games, the agents can withhold part of their endowment, namely consume whatever they do not deposit. In D-allocation games, the agents loose any part of their endowment that they do not put on the table, i.e., the agents can just destroy their endowments. We introduce Wand Dincentive compatible (I.C.) direct allocation mechanisms, in which every agent must simply report a type and make a deposit consistent with his reported type. We show that the revelation principle holds in full generality for D-I.C. mechanisms but that some care is needed for W-I.C. mechanisms. We further investigate the properties of both classes of mechanisms under common assumptions in implementation theory, namely non-exclusive information and/or constant aggregate endowment, and argue that many existing results implicitly require D-I.C. mechanisms. We establish that in T.U. economies, W-I.C. and D-I.C. mechanisms are ex ante equivalent. Key words: Bayesian implementation, exchange economy, incentive compatibility, mechanism design, revelation principle J.E.L. Classi…cation numbers: D82, D61, D78