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We study the problem of designing truthful and fair mechanisms whenallocating a mixture of divisible and indivisible goods. We first show thatthere does not exist an EFM (envy-free for mixed goods) and truthful mechanismin general. This impossibility result holds even if there is only oneindivisible good and one divisible good and there are only two agents. Thus, wefocus on some more restricted settings. Under the setting where agents havebinary valuations on indivisible goods and identical valuations on a singledivisible good (e.g., money), we design an EFM and truthful mechanism. Whenagents have binary valuations over both divisible and indivisible goods, wefirst show there exist EFM and truthful mechanisms when there are only twoagents or when there is a single divisible good. On the other hand, we showthat the mechanism maximizing Nash welfare cannot ensure EFM and truthfulnesssimultaneously.

Truthful Fair Mechanisms for Allocating Mixed Divisible and Indivisible Goods