论文标题
离散凸分析：经济学和游戏理论的工具
Discrete Convex Analysis: A Tool for Economics and Game Theory
论文作者
论文摘要
本文将离散凸分析作为经济学和游戏理论的工具。离散凸分析是在过去二十年中开发的离散数学和优化的新框架。最近，它被认为是分析具有不可分割性的经济或游戏模型的强大工具。离散凸分析的主要特征是对于整数或二进制变量中的功能，以及它们的共轭关系的两个凸度概念M-Convexity和l-convexity的区别。至关重要的事实是，M- con养或其称为M-Natural-Concavity的变体等同于经济学中的（总）替代财产。离散凸分析中的基本定理，例如M-L结合定理，离散的分离定理和离散的固定点定理在经济学中产生结构性结果，例如Eqeilibria的存在和平衡价格向量的晶格结构。离散凸分析中的算法提供了迭代拍卖算法以及平衡的计算方法。
This paper presents discrete convex analysis as a tool for economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, developed during the last two decades. Recently, it is being recognized as a powerful tool for analyzing economic or game models with indivisibilities. The main feature of discrete convex analysis is the distinction of two convexity concepts, M-convexity and L-convexity, for functions in integer or binary variables, together with their conjugacy relationship. The crucial fact is that M-concavity, or its variant called M-natural-concavity, is equivalent to the (gross) substitutes property in economics. Fundamental theorems in discrete convex analysis such as the M-L conjugacy theorems, discrete separation theorems and discrete fixed point theorems yield structural results in economics such as the existence of equilibria and the lattice structure of equilibrium price vectors. Algorithms in discrete convex analysis give iterative auction algorithms as well as computational methods for equilibria.
