AF: Small: Understanding the Behavior of Large Markets

New York University, New York NY

Investigators

Abstract

The Tragedy of the Commons indicates that at least in some circumstances the self-interested behavior of many individuals can lead to an outcome that is far from optimal. In contrast, the Invisible Hand of the Market suggests that in other settings, self-interested behavior leads to positive outcomes. What distinguishes these settings? One important differentiator is whether there is a diversity of interests. Another important ingredient is that the setting be large, in the sense that individual participants form only a small part of the setting (or the market, in particular). This project will be seeking to better understand large settings by quantifying the inefficiencies that arise due to self-interested behavior, and more specifically the rate at which these inefficiencies shrink as the setting size grows. The project will seek broadly applicable results, but will make this concrete by focusing on some specific settings including: (1) Price adjustment in market settings; one issue will be to identify when and why price adjustment algorithms lead to the desirable outcomes promised by the Invisible Hand. (2) Settings in which decisions do not involve payments, such as admissions to universities; the goal will be to develop plausible models which yield fair outcomes and which allow sensible student and university strategies to be explored. This genre of problem, involving human behavior together with computational concerns, appears to have broad appeal, both to undergraduate and graduate students; accordingly, the project will seek to involve students of all levels. While this notion of largeness has been well-studied in the economics field, this has been mainly in continuum settings or as in-the-limit results. In contrast, this project will seek quantifiable results, i.e. results that express a trade-off between the setting size and the quality of an outcome, and in particular settings for which there are polynomial trade-offs between the setting size and the quality of an outcome. One broad question is to identify conditions that allow continuum and in-the-limit results to be systematically converted to quantified results. More specific questions concern whether large market settings lead to robust versions of tatonnement (this is the family of price adjustment algorithms in which the price of a good is increased when the demand exceeds the supply, and reduced in the opposite case), robust in the sense that they are relatively parameter-free. The ultimate goal of this line of work is to provide an algorithmic explanation of price convergence to near-equilibrium states in a model which incorporates self-interested behavior. A second, quite distinct thrust will seek to explore conventional advice in large stable-matching-type settings, e.g., for students applying to college, namely advice such as: include one or two stretch schools and a safety school. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.