A Theory of Simplicity in Games and Mechanism Design

Abstract

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.

All sequential allotment rules are obviously strategy‐proof

“…Third, Pycia and Troyan (2022) propose a family of simplicity standards that depend on agents' ability to foresee further down in the game and that strengthen the notion of obvious strategy-proofness. Each standard brings about a notion of dominance and its correspondent of strategy-proofness.…”

“…See Mackenzie (2020) for a detailed description and discussion of the differences, similarities, and nuances between the proposals of those four papers. For other partially positive or revelation-principlelike results, see also Arribillaga, Massó, and Neme (2020), Bade and Gonczarowski (2017), Pycia andTroyan (2022), andTroyan (2019); note that although the first two papers also consider single-peaked preferences, they do so in the context of a public good (i.e., voting), while here the context is of private goods. 9 Mackenzie (2020) proves this for a class of extensive game forms with perfect information, called round table mechanisms, but the proof can be adapted to any extensive game form with perfect information.…”

“…22 The less simple standard is that in which agents can plan all their moves in the future, and it corresponds to Li's (2017) original OSP notion. Pycia and Troyan (2022) also focus on the standard of one-step dominance in which agents are able to plan at most one move ahead at a time, referred to as one-step simple. Given any sequential allotment rule , let us consider i's plan in of choosing today the best available assignment a i in A i ⊇ [[α i , β i ]] and choosing next time (if any) a i in A i ⊇ [[α i , β i ]] according to the following two possibilities: if a i = β + i , then a i = α i , while if a i = α − i , then a i = β i (note that if a i ∈ [[α i , β i ]], i does not move again).…”

Costly information acquisition in centralized matching markets

“…Li (2017) introduces the concept of obvious strategy‐proofness and shows that truth‐telling is an obviously dominant strategy under SeqSD, while this is not the case under DirSD. Pycia and Troyan (2019) show that SeqSD is the only mechanism which is efficient, fair, and obviously strategy‐proof. Li (2017) compares SeqSD and DirSD in the lab and finds that a significantly higher proportion of participants use the truth‐telling strategy under SeqSD than under DirSD.…”