信贷网络中的流动性：一点点信任就能发挥很大作用

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摘要翻译：
信用网络代表了网络中实体之间信任建模的一种方式。网络中的节点打印自己的货币，并相互信任对方一定数量的货币。这使得网络可以充当分散的支付基础设施--通过在信任节点之间传递各自货币的借据，可以将任意支付路由到网络中--并且避免了对共同货币的需要。节点之间可以重复进行交易，并使用可信货币支付交易费用。在这种情况下，一个自然的问题是：网络能维持多长时间的流动性，即在信贷枯竭之前，网络能支持多长时间的支付路径？我们用不同网络拓扑和信用值下交易的长期失败概率来回答这个问题。我们证明了事务失败概率与事务路由的路径无关。我们证明了在对称交易率下，随着网络规模、密度或信用容量的增加，许多知名图族中的交易失败概率趋于零。我们还通过仿真表明，即使是规模和信用容量较小的网络，如果它们之间连通良好，也可以以较高的概率路由交易。进一步，我们将集中式货币系统刻画为一种特殊类型的星型网络（其根的边具有无限的信用能力，交易只发生在叶节点之间），并计算了集中式货币系统的稳态交易失败概率。我们证明了星型网络、完备图和ERD{o}S-R'{e}nyi网络中的流动性与等价的集中货币系统中的流动性是相当的，因此我们不会因为它们的鲁棒性和分散性而损失太多的流动性。
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英文标题：
《Liquidity in Credit Networks: A Little Trust Goes a Long Way》
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作者：
Pranav Dandekar, Ashish Goel, Ramesh Govindan, Ian Post
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最新提交年份：
2012
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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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：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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英文摘要：
  Credit networks represent a way of modeling trust between entities in a network. Nodes in the network print their own currency and trust each other for a certain amount of each other's currency. This allows the network to serve as a decentralized payment infrastructure---arbitrary payments can be routed through the network by passing IOUs between trusting nodes in their respective currencies---and obviates the need for a common currency. Nodes can repeatedly transact with each other and pay for the transaction using trusted currency. A natural question to ask in this setting is: how long can the network sustain liquidity, i.e., how long can the network support the routing of payments before credit dries up? We answer this question in terms of the long term failure probability of transactions for various network topologies and credit values.   We prove that the transaction failure probability is independent of the path along which transactions are routed. We show that under symmetric transaction rates, the transaction failure probability in a number of well-known graph families goes to zero as the size, density or credit capacity of the network increases. We also show via simulations that even networks of small size and credit capacity can route transactions with high probability if they are well-connected. Further, we characterize a centralized currency system as a special type of a star network (one where edges to the root have infinite credit capacity, and transactions occur only between leaf nodes) and compute the steady-state transaction failure probability in a centralized system. We show that liquidity in star networks, complete graphs and Erd\"{o}s-R\'{e}nyi networks is comparable to that in equivalent centralized currency systems; thus we do not lose much liquidity in return for their robustness and decentralized properties.
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PDF链接：
https://arxiv.org/pdf/1007.0515

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关键词：流动性 Transactions Quantitative Applications Coordination 交易 失败 each liquidity 证明