We introduce the study of designing allocation mechanisms for fairly allocating indivisible goods in settings with interdependent valuation functions. In our setting, there is a set of goods that needs to be allocated to a set of agents (without disposal). Each agent is given a private signal, and his valuation function depends on the signals of all agents. Without the use of payments, there are strong impossibility results for designing strategyproof allocation mechanisms even in settings without interdependent values. Therefore, we turn to design mechanisms that always admit equilibria that are fair with respect to their true signals, despite their potentially distorted perception. To do so, we first extend the definitions of pure Nash equilibrium and well-studied fairness notions in literature to the interdependent setting. We devise simple allocation mechanisms that always admit a fair equilibrium with respect to the true signals. We complement this result by showing that, even for very simple cases with binary additive interdependent valuation functions, no allocation mechanism that always admits an equilibrium, can guarantee that all equilibria are fair with respect to the true signals.

翻译：我们引入了在具有相互依赖估值函数的环境中设计公平分配不可分割物品机制的研究。在我们的设定中，存在一组需要分配给一组代理人的物品（不允许销毁）。每个代理人获得一个私人信号，其估值函数依赖于所有代理人的信号。在不使用支付的情况下，即使在没有相互依赖估值的环境中，设计防策略分配机制也存在强不可能性结果。因此，我们转向设计始终存在均衡的机制，这些均衡相对于代理人的真实信号是公平的，尽管其感知可能存在扭曲。为此，我们首先将纯纳什均衡和文献中广泛研究的公平性概念扩展到相互依赖设定中。我们设计了简单的分配机制，这些机制始终存在相对于真实信号的公平均衡。我们通过证明即使是在具有二元可加相互依赖估值函数的极简情形中，没有任何始终存在均衡的分配机制能保证所有均衡相对于真实信号都是公平的，来补充这一结果。