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 destroypart 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.
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