AF: Small: Understanding the Behavior of Large Markets

公地的悲剧表明，至少在某些情况下，许多人的自利行为可能导致远非最佳结果。相比之下，《看不见的市场之手》表明，在其他情况下，自利行为会带来积极的结果。这些设置有什么不同之处？一个重要的区别因素是，是否存在不同的利益。另一个重要因素是，背景是大的，从这个意义上说，个人参与者只构成背景(或特别是市场)的一小部分。这个项目将寻求通过量化由于自利行为而产生的低效，更具体地说，这些低效随着环境规模的增长而缩小的速度，来更好地理解大型环境。该项目将寻求广泛适用的结果，但将通过侧重于一些具体环境来具体实现这一点，包括：(1)市场环境中的价格调整；其中一个问题将是确定价格调整算法何时以及为什么导致看不见的手承诺的理想结果。(2)决策不涉及支付的环境，如大学录取；目标将是开发出合理的模式，产生公平的结果，并允许探索合理的学生和大学战略。这类涉及人类行为和计算问题的问题似乎对本科生和研究生都有广泛的吸引力；因此，该项目将寻求涉及所有水平的学生。虽然这种大的概念在经济学领域已经得到了很好的研究，但这主要是在连续统环境下或作为有限的结果。相反，该项目将寻求可量化的结果，即表达背景大小和结果质量之间权衡的结果，特别是在背景大小和结果质量之间存在多项式权衡的背景。一个广泛的问题是确定允许连续的和限定的结果被系统地转换为量化结果的条件。更具体的问题涉及大型市场环境是否会导致稳健的纹身版本(这是一系列价格调整算法，当供不应求时，商品的价格会增加，反之，商品的价格就会降低)，稳健的意义在于它们相对不受参数的影响。这项工作的最终目标是在一个包含自利行为的模型中提供价格收敛到接近均衡状态的算法解释。第二，相当独特的重点将寻求在大型稳定匹配类型的环境中探索传统建议，例如针对申请大学的学生的建议，即：包括一到两所延伸学校和一所安全学校。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.