Obviously strategy-proof implementation for mixed-ownership object-allocation problems

We study the problem of allocating indivisible commodities, or “objects”, when some of them are privately owned and some are collectively owned. We search for well-behaved rules that are implementable in “obviously dominant equilibrium”, namely, obviously strategy-proof rules (Li, 2017). We start from the you request my house–I get your turn rules (Abdulkadiroǧlu and Sönmez, 1999), the “AS rules”. We ask whether and when they are obviously strategy-proof. When preferences are strict but otherwise unrestricted, and with at least three agents, the AS rules are obviously strategy-proof if and only if there is at most one owner. This disappointing result raises the question whether things would work out better on some restricted preference domains. On the single-peaked domain, we propose a new family of rules and show that not only are these “priority-augmented crawlers” obviously strategy-proof, but also that they satisfy efficiency, the individual endowments lower bounds, group strategy-proofness, weak neutrality, and separability. On the single-dipped domain, we establish a contrasting result: on this subdomain, unlike on the single-peaked domain, the AS rules are obviously strategy-proof.