Fair division with interdependent values

We investigate the design fair allocation mechanisms for indivisible goods in settings where agents’ valuations are interdependent. 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. An allocation mechanism for the interdependent settings receives a report from every agent that includes their own signals, and outputs an allocation (with no payments). 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 a weaker notion of incentive, where we 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.