Abstract: 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 attention in the management science or operations management literature. This survey is deployed along three dimensions 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 agents. 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 competition. Most of the models are in game theoretic framework, including Cournot-Nash equilibrium, Bertrand-Nash equilibrium, Stackelberg game. But network economic models such as spatial price equilibrium and Wardrop equilibrium are also proved to be powerful and effective means for modeling supply chain versus supply chain competition. 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 between 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.