Choosing (as if) from a menu (by Gonczarowski, Heffetz and Thomas; and by Bó, and Hakimov)

What makes serial dictatorship so obviously strategy proof is that it gives each participant the opportunity to choose from a menu, and get what he/she picks.  So the dominant strategy is to pick what you want (and if you have to delegate the decision by submitting a list of preferences, it is a dominant strategy to state your true preferences.

Here are two papers differently inspired by that thought, which seek to reformulate matching mechanisms so that they look to each player like choice from a menu.

Strategyproofness-Exposing Mechanism Descriptions by Yannai A. Gonczarowski, Ori Heffetz, Clayton Thomas

Abstract: "A menu description defines a mechanism to player i in two steps. Step (1) uses the reports of other players to describe i's menu: the set of i's potential outcomes. Step (2) uses i's report to select i's favorite outcome from her menu. Can menu descriptions better expose strategyproofness, without sacrificing simplicity? We propose a new, simple menu description of Deferred Acceptance. We prove that -- in contrast with other common matching mechanisms -- this menu description must differ substantially from the corresponding traditional description. We demonstrate, with a lab experiment on two simple mechanisms, the promise and challenges of menu descriptions."

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Pick-an-object Mechanisms by Inácio Bó, Rustamdjan Hakimov

Abstract: "We introduce a new family of mechanisms for one-sided matching markets, denoted pick-an-object (PAO) mechanisms. When implementing an allocation rule via PAO, agents are asked to pick an object from individualized menus. These choices may be rejected later on, and these agents are presented with new menus. When the procedure ends, agents are assigned the last object they picked. We characterize the allocation rules that can be sequentialized by PAO mechanisms, as well as the ones that can be implemented in a robust truthful equilibrium. We justify the use of PAO as opposed to direct mechanisms by showing that its equilibrium behavior is closely related to the one in obviously strategy-proof (OSP) mechanisms, but implements commonly used rules, such as Gale-Shapley DA and top trading cycles, which are not OSP-implementable. We run laboratory experiments comparing truthful behavior when using PAO, OSP, and direct mechanisms to implement different rules. These indicate that agents are more likely to behave in line with the theoretical prediction under PAO and OSP implementations than their direct counterparts."