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A compositional approach to game-theoretic economic modelling

博弈论经济建模的组合方法

基本信息

批准号：
EP/N021282/1
负责人：
Julian Hedges
金额：
$ 33.04万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FN021282%2F1
关键词：
compositional approach game theoretic economic

项目摘要

Game theory is the mathematical study of strategic interaction and decision-making under uncertainty. It is arguably the central tool of microeconomics, and is also widely used in evolutionary biology, cybersecurity and military strategy, among other application areas. Compositionality, one of the most fundamental ideas of software science, is the principle that the behaviour of a system should be understandable in terms of the behaviour of its components. Compositionality allows large, complex systems to be designed, implemented, analysed and tested in a modular way, and allows modules to be reused in different contexts. Without this, modern software engineering would be impossible.Game models, however, are not compositional, and generally must be produced in their entirety rather than by combining standard components. As a result, game-theoretic modelling is a slow process, as small variations in the domain to be modelled can lead to large changes needed in the model. In particular this means that game-theoretic models are currently not well-suited to software implementation.This project concerns a new approach to game theory which is compositional, and therefore promises the possibility of software support for economists and other users of game theory on a scale that is currently impossible. Specifically, it should be possible to specify, simulate, solve and more generally reason about games in a way that allows the reuse of existing work. For example a typical economic system has a hierarchical structure, from agents to households to markets to economies, and it should be possible to gradually build models of each level in a way that directly uses existing models of the lower levels.The mathematical techniques and concepts underlying this approach mostly come from proof theory (part of mathematical logic) and the theory of programming languages (part of theoretical computer science). Fortunately there is no need for users to learn this sophisticated and (to them) unfamiliar theory, because it is also possible to hide the mathematics behind an intuitive graphical language known as string diagrams, which have been widely studied recently due to applications in quantum information theory, linguistics and abstract algebra. This means that game theoretic software can be graphical and intuitive, but still have a strong theoretical underpinning.The purpose of this project is to develop the mathematical theory needed for these economic applications, in a way that exploits the close relationship between theory and applications in this area, while using a worked example (based on modelling of smart energy grids) to provide a continual test of the practical benefits of compositionality.A large part of the theoretical part of this project will involve extending the theory of selection functions with various known concepts in game theory, such as repeated games, imperfect information and different solution concepts, which can be found in any standard text on game theory. This will largely consist of generalising existing theory to the new framework.

博弈论是对不确定性下的战略互动和决策的数学研究。它可以说是微观经济学的核心工具，也被广泛用于进化生物学，网络安全和军事战略等应用领域。组合性是软件科学最基本的思想之一，它是一个原则，即系统的行为应该根据其组件的行为来理解。组合性允许以模块化的方式设计、实现、分析和测试大型复杂系统，并允许在不同的上下文中重用模块。没有这些，现代软件工程将是不可能的。然而，游戏模型不是组合的，通常必须完整地生成，而不是通过组合标准组件。因此，博弈论建模是一个缓慢的过程，因为要建模的领域中的小变化可能导致模型中需要的大变化。特别是这意味着，博弈论模型目前不适合软件implementation.This项目涉及一种新的方法，博弈论是组合，因此承诺的可能性，软件支持经济学家和其他用户的博弈论的规模，目前是不可能的。具体来说，它应该可以指定，模拟，解决和更普遍的原因，游戏的方式，允许重用现有的工作。例如，一个典型的经济系统有一个等级结构，从代理人到家庭到市场到经济体，这种方法的数学技术和概念主要来自于证明理论（数理逻辑的一部分）和编程语言理论（理论计算机科学的一部分）。幸运的是，用户不需要学习这个复杂的和（对他们来说）不熟悉的理论，因为它也可以隐藏数学背后的直观图形语言称为弦图，最近由于量子信息理论，语言学和抽象代数的应用而被广泛研究。这意味着博弈论软件可以是图形和直观的，但仍然有一个强大的理论基础。这个项目的目的是开发这些经济应用所需的数学理论，在某种程度上，利用理论和应用之间的密切关系，在这个领域，当使用一个工作的例子时，（基于智能能源网模型）提供一个连续的测试的实际利益的组合。一个大部分的理论部分，这个项目将涉及扩展理论的选择功能与各种已知的概念在博弈论中，如重复博弈，不完全信息和不同的解决方案的概念，这可以在任何标准的文本博弈论。这将主要包括将现有理论推广到新的框架。