Mechanism Design With Limited Commitment

Abstract

We develop a tool akin to the revelation principle for dynamic mechanism‐selection games in which the designer can only commit to short‐term mechanisms. We identify a canonical class of mechanisms rich enough to replicate the outcomes of any equilibrium in a mechanism‐selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. Our result simplifies the search for the designer‐optimal outcome by reducing the agent's behavior to a series of participation, truth telling, and Bayes' plausibility constraints the mechanisms must satisfy.

Optimal mechanism for the sale of a durable good

“…Lemma 1 (Doval and Skreta (2022)). For any PBE outcome of any mechanism-selection game G I (μ 0 ), an outcome-equivalent PBE of game G(μ 0 ) exists.…”

“…7 Because V is finite, taking M M to be finite is without loss of generality (Doval and Skreta, 2022). 8 We restrict the seller to choose mechanisms with input and output messages in (M i , S i ) i∈I to have a well-defined action space for the seller.…”

“…A direct Blackwell mechanism is a canonical mechanism ϕ : V → ( (V ) × A) that can be decomposed into a Blackwell experiment, β : V → ( (V )), and an allocation rule, α : (V ) → (A). 11 Lemma 1 summarizes the key implications of Doval and Skreta (2022) for our analysis, which we explain below.…”

Slow persuasion

“…This paper belongs to the Bayesian persuasion literature initiated by Kamenica and Gentzkow (2011), Rayo and Segal (2010) and Aumann and Maschler (1995) (see Kamenica (2019) and Bergemann and Morris (2019) for surveys). We contribute in particular to the growing strand of that literature which examines the impact of constraints on (or costs of) information production (e.g., Gentzkow and Kamenica (2014), le Treust and Tomala (2019) and Doval and Skreta (2021)) 2 . Whereas these papers consider static settings, we study a dynamic constraint: graduality.…”

“…22 Some of this work is surveyed by Kamenica, Kim, and Zapechelnyuk (2021). Calzolari and Pavan (2006a,b), Pavan and Calzolari (2009), Rosar (2017), Georgiadis and Szentes (2020), Dworczak (2020), Doval and Skreta (2021) and Boleslavsky and Kim (2021) study persuasion problems subject to incentive constraints. …”