凹广义流及其在市场均衡中的应用

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摘要翻译：
我们考虑了Truemper和Shigeno提出的广义网络流模型的非线性推广，其中离开弧的流是进入弧的流的增凹函数。给出了求解相应的流最大化问题的多项式时间组合算法，在O(m(m+logn)log(mum/epsilon))算术运算和值oracle查询中求ε近似解，其中m和U是简单参数的上界。这也给出了线性广义流的一个新算法，它是Goldberg、Plotkin和Tardos的脂肪路径算法的一个有效的纯尺度变体，不使用任何循环抵消。我们证明了这个一般凸规划模型是几个市场均衡问题的通用框架，包括线性Fisher市场模型及其各种扩展。我们的结果立即将这些市场模型扩展到更一般的环境。我们还得到了一个非对称Arrow-Debreu-Nash讨价还价的组合算法，解决了Vazirani提出的一个公开问题。
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英文标题：
《Concave Generalized Flows with Applications to Market Equilibria》
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作者：
Laszlo A. Vegh
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Data Structures and Algorithms        数据结构与算法
分类描述：Covers data structures and analysis of algorithms. Roughly includes material in ACM Subject Classes E.1, E.2, F.2.1, and F.2.2.
涵盖数据结构和算法分析。大致包括ACM学科类E.1、E.2、F.2.1和F.2.2中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsilon-approximate solution in O(m(m+log n)log(MUm/epsilon)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters. This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg, Plotkin and Tardos, not using any cycle cancellations.   We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately extends these market models to more general settings. We also obtain a combinatorial algorithm for nonsymmetric Arrow-Debreu Nash bargaining, settling an open question by Vazirani.
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PDF链接：
https://arxiv.org/pdf/1109.3893

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关键词：市场均衡 Applications maximization cancellation Coordination model 提出 离开 广义 problems