Feasible mechanisms in economies with type-dependent endowments

We propose two classes of allocation games for N.T.U. and T.U. exchange economies in which initial endowments and preferences depend on the agents' private information. In both models, agents make non-verifiable claims about their types and effective deposits of consumption goods, which are redistributed by the planner. In a W-allocation game, the agents can withhold part of their endowment, namely consume whatever they do not deposit. In a D-allocation game, the agents can just destroy part of their endowment. W- and D- incentive compatible (I.C.) direct allocation mechanisms ask every agent to reveal his type and to make a deposit consistent with his reported type. The revelation principle holds in full generality for D-I.C. mechanisms but some care is needed for W-I.C. mechanisms. We further investigate the properties of both classes of mechanisms under common assumptions like non-exclusive information and/or constant aggregate endowment. In T.U. economies, W-I.C. and D-I.C. mechanisms are ex ante equivalent.