文章基本信息

标题：Discrete convex analysis: A tool for economics and game theory
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作者：Kazuo Murota
期刊名称：Journal of Mechanism and Institution Design
印刷版ISSN：2399-844X
电子版ISSN：2399-8458
出版年度：2016
卷号：1
期号：1
页码：149-271
DOI：10.22574/jmid.2016.12.005
摘要：This paper presents discrete convex analysis as a tool for use in economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, developed during the last two decades. Recently, it has been 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 in its variant 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 provide iterative auction algorithms for finding equilibria.
关键词：Convex analysis; indivisibility; equilibrium; fixed point.