中文摘要：

本文试图从供应链的结构、竞争的数学经济模型，以及工业应用的领域等三个方向，概括和介绍国际和国内有关供应链链际竞争的研究工作。其中绝大多数的数学模型是建立在竞争的各方都是具有相同性质和相同结构的供应链的前提假设下，因此是对称的链际竞争模型，而且主要局限于二层或者三层的供应链网络。但是我们也特别介绍了一些非对称的模型可以用来研究不同性质和结构的供应链之间的竞争问题。另一个有意义的方向是研究链内的合作契约在链际竞争中所起到的作用。

英文摘要：

This paper provides a limited survey on mathematical models of inter supply chain competition, a topic whose importance is widely recognized in business and industry but not until recently has gained adequate atten- tion in the management science or operations management literature. This survey is deployed along three dimen- sions of the literature collected on this topic. We first classify the works based on the network structure of the competing supply chains, ranging from the simplest one-supplier-one-retailer chain, through three-tier symmetric network with multiple agents on each tier, to most general asymmetric network structure with any number of a- gents. The symmetric network is termed to refer the competition between homogeneous structured supply chains, whereas asymmetric network is termed to refer the competition between heterogeneous structured supply chains. Secondly, we review the mathematical and economic models employed to study the inter supply chain competi- tion. Most of the rnodels are in game theoretic framework, including Cournot-Nash equilibrium, Bertrand-Nash e- quilibrium, Stackelberg game. But network economic models such as spatial price equilibrium and Wardrop e- quilibrium are also proved to be powerful and effective means for modeling supply chain versus supply chain com- petition. Thirdly, we thread the relevant works in various application areas. The application background of these models range from power supply chain, financial supply chain, environment and corporate social responsibilities, reverse logistics, and automobile industry supply chains. The majority of these works study the competition be- tween chains of same nature and homogeneous structure. But emerging models on inter chain competition between heterogeneous chains are remarkable. Another noticeable progress is represented by incorporating intra chain contract into inter chain competition.