Two-sided allocation problems, decomposability, and the impossibility of efficient trade

Abstract

Previous literature has shown that private information is a transaction cost that prevents efficient reallocation in two-sided setups with bilateral trade or homogeneous goods. We derive conditions under which the impossibility of efficient trade extends to rich environments in which buyers and sellers have multi-dimensional private types, accommodating many-to-many trades and heterogeneous objects. If agents can be decomposed into unit constituents, the allocation problem can be represented as an assignment game and impossibility obtains through a generalization of Shapley's (1962) result that buyers and sellers are complements. We introduce a general family of payoff functions that ensures decomposability and thus impossibility.

Quantile Stable Mechanisms

“…We can also generalize this example to a many-to-many matching market. For further analysis of the endowment assignment model, see Delacretaz et al [30]).…”

Two‐sided service markets: Effects of quality differentiation on market efficiency

“…Third, the mechanism must not run a permanent deficit in funds (budget balance). However, mechanism design theory corroborates that ex post efficiency is not attainable for mechanisms requiring these properties simultaneously (Delacrétaz, Loertscher, Marx, & Wilkening, 2019; Laffont & Maskin, 1979; Myerson & Satterthwaite, 1983). Because ex post efficiency is unattainable, the literature suggests to derive so‐called second‐best mechanisms , which maximize the expected social welfare while maintaining the three desired properties based on appropriate solution concepts (Bierbrauer, Ockenfels, Pollak, & Rückert, 2017; Gresik & Satterthwaite, 1989; Segal & Whinston, 2016).…”

Comparative statics for size-dependent discounts in matching markets

“…1 Introduction Delacrétaz et al (2019) introduced a general family of valuation functions with sizedependent discounts, under which each agent's value for sets of potential partners is given by an additive valuation over individual agents, discounted by a term that depends on the total number of agents in the set. 1 The additivity of a's valuations ensures that each agent with whom a may partner is evaluated independently from any other agent in the set; thus, there are no externalities among potential partners.…”

“…For simplicity, with some abuse of notation, we write v a δ instead of v a δ a . 4 Our size-dependent discounts condition corresponds to the "one block" non-monotonic version ofDelacrétaz et al (2019).…”

“…Valuations with size-dependent discounts also appear in auction/procurement settings(Delacrétaz et al, 2019).6 For a recent survey of the matching with constraints literature, seeKamada and Kojima (2017).7 To embed hard constraints, such as a school's maximal physical capacity N + n, it suffices to set the discount term δ N +n+1 to a very high value (in this case, larger than the highest possible score).8 The general family of valuation functions with size-dependent discounts of Delacrétaz et al (2019) allows for various "blocks" of objects, where each block corresponds to, e.g., a different commodity Ehlers et al (2014). allowed for various student types that may be determined by, e.g., ethnicity or some other socioeconomic criteria.…”