Welfare-maximizing assignment of agents to hierarchical positions

Abstract

a b s t r a c tWe allocate agents to three kinds of hierarchical positions: top, medium, and low. No monetary transfers are allowed. We solve for the incentive-compatible (IC) mechanisms that maximize a family of weighted social welfares that includes utilitarian and Rawlsian welfares. When the market is tough (all agents bear positive risk of obtaining a low position in any IC and feasible mechanism), then the pseudomarket mechanism with equal budgets (PM) and the Boston mechanism without priorities (BM) yield identical assignments which are always optimal. Otherwise, when the market is mild, PM and BM differ and each one implements the optimal rule under different assumptions on the curvature of virtual valuations. We also establish that both BM and PM mechanisms guarantee IC Pareto-optimal assignments for a domain of preference distributions satisfying weak assumptions.

Optimal assignment mechanisms with imperfect verification

“…Dogan and Uyanik (2020) study a simplified version of Miralles (2012) and, like us, find that wasteful allocation rules might be optimal. Hafalir and Miralles (2015) and Ortoleva, Safonov, and Yariv (2021) consider models with a continuum of agents and find optimal mechanisms that have features similar to ours. Specifically, agents who have high valuations receive lotteries over objects where there is a large probability of receiving high-quality objects, but also a high probability of receiving low-quality objects, while agents with low valuations receive lotteries with a high probability of receiving average quality objects.…”

“…Even though agents have the same ordinal preferences over objects, the fact that they have different cardinal preferences leads to them having different preferences over lotteries of objects. Building on this insight, several authors have used mechanism design techniques to study the problem of finding welfare maximizing incentive compatible allocation rules in settings where agents have common ordinal preferences (Miralles (2012), Hafalir and Miralles (2015), Dogan and Uyanik (2020), Ortoleva, Safonov, and Yariv (2021)).…”

Foundations of pseudomarkets: Walrasian equilibria for discrete resources

“…It turns out that in general a feasible random assignment of bundles that is strongly efficient might not exist. 27 However, it does exist when preferences over bundles are strict and since this is a generic property so is the existence of strongly efficient assignments.…”

“…Our model allows for many design constraints such as e.g. reserving some seats in a school for a group of applicants, while allowing all applicants to compete for the remaining seats; 27 We illustrate it in the following example that builds on the first example and the proposition of this section. Recall that…”

Prices and Efficient Assignments Without Transfers

“…Token money mechanisms have been extended beyond the canonical Hylland and Zekchauser setting by, for instance, Sonmez and Unver (2010), Budish (2013), Manjunath (2014), and Miralles (2014). Hafalir and Miralles (2014) analyze the utilitarian e ciency of such market approaches. None of these papers establishes a Second Welfare Theorem.…”