Markets and Other Robust Self-Governing Systems

自然算法是存在于自然界和社会中的过程，这些过程似乎没有被明确设计或编程。 通常情况下，人们从随之而来的结果（如经济市场中的供求平衡）推断出这种过程的存在，而不是从对过程的明确介绍（如价格调整程序）中推断出这种过程的存在。 出现了两个问题：进程是什么（即它们采取什么步骤），它们的能力和局限性是什么？ 这个项目从计算的角度来处理这个问题。主要关注经济市场均衡，它可以被描述为平衡供应和需求的价格。 人们普遍认为，经济市场往往会在扰动之后恢复到平衡状态，这里研究的问题是何时可能恢复到平衡状态。 因此，上面的第一个问题相当于问市场中可能发生什么价格调整才能导致这种情况发生;第二个问题问的是，实际上，这些调整何时能导致向均衡收敛，如果收敛可以发生，速度有多快？在以前的工作中，提出了一种新的方法，将时间在标准的市场模型，这似乎是建模和分析价格调整协议的必要性。 本项目旨在从多个维度发展这种分析，即：（1）解释商品和货币的离散性，（2）处理动态环境，（3）提供参与者行为的战略解释，（4）纳入生产，（5）分析弱总量替代假设不成立的（一些）环境。 最后，该项目将寻求为其他自然和其他自治系统（例如生物系统和网络路由）进行类似的解释和分析。

Natural algorithms are processes that exist in nature and society, processes that do not appear to be explicitly designed or programmed. Typically, one infers the existence of such processes from the results that ensue (e.g. supply and demand balancing in an economic market) as opposed to an explicit presentation of the process (e.g. a procedure for price adjustment). Two questions arise: what are the processes (i.e. what steps do they undertake) and what are their capabilities and limitations? This project approaches the issue from a computational perspective.The main focus will be on economic market equilibria, which can be characterized as prices that balance supply and demand. It is widely believed that economic markets tend to revert to equilibrium states following disturbances, and the issue studied here is when this might be possible. So the first question above amounts to asking what price adjustments might occur in markets to cause this to happen; the second question asks when, in fact, can these adjustments cause convergence to equilibrium, and if convergence can occur, how fast is it?In prior work, a new way of incorporating time in the standard market models was proposed; this seems a necessity for modeling and analyzing price adjustment protocols. This project aims to develop that analysis in multiple dimensions, namely: (1) to account for discreteness of goods and money, (2) to handle dynamic environments, (3) to provide strategic explanations of participant behavior, (4) to incorporate production, (5) to analyze (some) environments in which the Weak Gross Substitutes assumption does not hold. Finally, the project will seek to develop analogous explanations and analyses for other self-governing systems, natural and otherwise, for example in biological systems and in network routing.