We identify necessary and sufficient conditions under which a coarse data set can be coarsely rationalized by a linear order (or weak order). The conditions are easy to check, and efficient algorithms are provided. We apply our theory to investigate the observable restrictions of several...

We develop an extension of Luce's random choice model that incorporates a role for the association of alternatives. Each alternative is characterized by a salience value, a Luce value, and its associated alternatives. The salience value captures the alternative's ability to attract the decision...

Motivated by the literature on random choice and in particular the random utility models, we extend the analysis in Bossert and Sprumont (2013) to include the possibility that players exhibit stochastic preferences over alternatives. We prove that every random choice rule is backwards-induction...

A principal has n homogeneous objects to allocate to I n agents. The principal can allocate at most one good to an agent and each agent values the good. Agents have private information about the principal's payoff of allocating the goods. There are no monetary transfers but the principal can...

We provide a framework for studying two-sided matching markets with incomplete information. The framework accommodates two-sided incomplete information as well as heterogeneous information among the agents. We propose a notion called stability for a market state, which, based upon agents'...

This paper studies a matching algorithm which is termed incomplete-information deferred acceptance (DA). We show that DA is finite and that it produces a stable market state. We also compare DA with algorithms in the literature, including the complete-information Gale-Shapley algorithm, the...

This paper extends the Bayesian stability notion of Liu (2020) to define the Bayesian stability of a market state , which consists of a matching outcome and an information structure. Here, the information structure can be arbitrarily heterogeneous among agents. We first establish that Liu’s...

A principal who values an object allocates it to one or more agents. Agents learn private information (signals) from an information designer about the allocation payoff to the principal. Monetary transfer is not available but the principal can costly verify agents' private signals. The...

In this paper, we extend the stability notion and Bayesian efficiency notion of Liu (2020) to local ones, as well as his result—that under certain intuitive conditions, stable matchings are Bayesian efficient—to an analogous one for local notions. Furthermore, the extended stability notion,...

We define and investigate a property of mechanisms that we call “strategic simplicity,” and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices are easy. We define a mechanism to be strategically simple if strategic choices can be based on...