Random Priority is a popular mechanism used to allocate a set of objects to a set of agents without the use of monetary transfers. Random Priority is appealing because it satisfies desirable efficiency, fairness, and incentive properties. Is it the only mechanism with these properties? We answer this long‐standing question in the positive: Random Priority is the unique mechanism that is Pareto efficient, symmetric, and obviously strategy‐proof.

We study extensive‐form games and mechanisms allowing agents that plan for only a subset of future decisions they may be called to make (the planning horizon ). Agents may update their so‐called strategic plan as the game progresses and new decision points enter their planning horizon. We introduce a family of simplicity standards which require that the prescribed action leads to unambiguously better outcomes, no matter what happens outside the planning horizon. We employ these standards to explore the trade‐off between simplicity and other objectives, to characterize simple mechanisms in a wide range of economic environments, and to delineate the simplicity of common mechanisms such as posted prices and ascending auctions, with the former being simpler than the latter.