We consider the problem of allocating several homogeneous indivisible goods when monetary transfers among agents are possible. We study the possibility of constructing strategy-proof and Pareto efficient mechanisms on restricted domains of agents’ valuation profiles. We show that there is no strategy-proof and Pareto efficient mechanism under the weak domain condition that all agents’ sets of possible valuations share at least four common valuations satisfying a certain inequality. Moreover, we prove that this impossibility result is robust to any affine transformation of domains, and we examine this impossibility result when the set of agent’s possible valuations consists of finite integers.

当代理商之间进行货币转移时，我们考虑分配几种同质的不可分割货物的问题。我们研究了在代理商评估资料的受限域上构建策略验证和帕累托有效机制的可能性。我们表明，在弱域条件下，即所有代理商的可能估值集共享至少四个满足一定不平等性的共同估值，在弱域条件下没有策略证明和帕累托高效机制。此外，我们证明了这种可能性结果对于域的任何仿射变换都具有鲁棒性，并且当代理的可能估值集合由有限整数组成时，我们检验了这种可能性结果。