AF:Small:Markets, Allocations and Dynamics

对资源分配的需求无处不在。通常，它涉及利益冲突的参与者。尽管存在这种利益冲突，但市场和拍卖都有助于产生理想的结果，但当金钱无法交换时(例如在肾脏交换中)，就会使用其他机制。一个重要的目标是找到稳定的结果，即个体参与者在无法改善结果的意义上对结果感到满意的结果；这些结果被称为均衡。对于现有的环境，如经济市场和广泛使用的机制(例如，互联网路由协议或主要搜索引擎使用的通用第二价格拍卖)，人们希望了解现有机制的运行情况。具体地说，(I)在什么情况下存在均衡结果？(Ii)能否找到它们(或接近均衡)？(3)均衡结果可信吗？即，由于该机制引起的相互作用，是否似乎合理地实现了均衡结果？这项研究将侧重于匹配市场，特别是住房市场。在其他没有现有机制或引入新机制的成本不高的情况下，人们可以寻求设计产生理想结果的机制。这项研究将集中在可分割商品(即可以分割成多个部分的商品)的分配上。匹配市场的标准建模，如住房市场，假设买家有严格的预算限制。不幸的是，当这一假设成立时，可能没有均衡的解决方案。相反，这项研究将考虑基于剩余财富的自然软预算限制，这是一种保证均衡的设置。主要问题是，在这种背景下，均衡是否是结果的预测因素。研究的必要条件是，均衡可以有效地计算，近似均衡接近实际均衡，这些近似均衡可能是买卖双方行为的结果。在机制设计方面，作为标准，本研究将寻求真实的机制，即没有激励参与者制定战略的机制。换句话说，参与者将通过诚实地申报(例如，他们对不同可能的分配的估值)来实现其最佳结果。一般来说，不可能使用真实的机制来分配所有资源。相反，这项研究旨在了解分配不足但真实的机制所产生的解决方案的质量。特别是，本研究旨在研究一类比例公平机制，这类机制最初是在互联网路由的背景下引入的。

The need for resource allocation is pervasive. Often, it involves participants with conflicting interests. Markets and auctions both serve to produce desirable outcomes despite such conflicting interests, and yet other mechanisms are used when money cannot be exchanged (e.g. in kidney exchanges). An important goal is to find stable outcomes, outcomes with which individual participants are content in the sense that they cannot improve the outcome; these outcomes are called equilibria.For existing settings, such as economic markets and widely used mechanisms (e.g. Internet routing protocols or the Generalized Second Price auction used by major search engines), one wants to understand how well the existing mechanisms work. Specifically (i) In what settings are there equilibrium outcomes? (ii) Can they (or near-equilibria) be found? (iii) Are the equilibrium outcomes plausible, i.e. does it seem reasonable that they will be reached due to the interactions induced by the mechanism? This research will focus on matching markets and the housing market in particular.In other settings, where there are no existing mechanisms or the costs of introducing new mechanisms are not prohibitive, one can seek to design mechanisms that produce desirable outcomes. This research will focus on the allocation of divisible goods (i.e. goods that can be split into many parts).The standard modeling of matching markets, such as the housing market, assumes buyers have sharp budget limits. Unfortunately, when this assumption holds there may be no equilibrium solution. Instead, this research will consider a natural soft budget limit based on residual wealth, a setting where equilibria are guaranteed. The main issue is whether equilibria in this setting are predictors of outcomes. Necessary conditions, which will be investigated, are that the equilibria can be computed efficiently, that approximate equilibria are close to the actual equilibria, and that these approximate equilibria could arise as a result of the actions of buyers and sellers.With regard to mechanism design, as is standard, this research will seek truthful mechanisms, mechanisms which give participants no incentive for strategizing. In other words, participants will achieve their best outcomes by making honest declarations (e.g. of their valuations for different possible allocations). In general, it is not possible to allocate all the resources using truthful mechanisms. Instead, this research aims to understand the quality of the solutions produced by under-allocating yet truthful mechanisms. In particular, this research intends to study the class of proportionally fair mechanisms, mechanisms which were first introduced in the context of internet routing.