There are two basic types of barter, i.e., personal barter and re- tail barter or commercial barter between companies. For example,U-Exchange is a personal barter platform for exchanging various products and services. BookMooch and Home Exchange are personal barter platforms for bartering books and apartments, respectively. We can also find some commercial barter platforms such as iBarter, IMS Barter, b2b-barter, and barterxyz. In this paper we focus only on commercial barter. The trade sequence of barter ex- change goes is as follows: Firm A registers on a barter exchange platform and provides some essential information, including what product and how many it will put up for barter? What’s the price? And what product it needs? The broker of the platform will help Firm A to find Firm B that exactly needs the product of Firm A and that provides the product that Firm A exactly needs. Then Firm A and B can trade their product without money, and pay the broker a commission that typically is about 5%-15% of the trade value. The collection of barter trade exchange is called the barter pool. In modern barter exchanges, if the broker cannot find a single Firm B for Firm A, e.g., Firm B needs the product of Firm A, but Firm A does not need the product of Firm B, it can find more firms to conduct a multilateral barter, which involves more than two firms. Suppose that Firm C exactly needs the product of Firm B, and Firm A needs the product of Firm C, then the trade is consummated. Multilateral barter exchanges which are conducted through cycles or chains is one of the typical characteristics of the modern barter . Another typical characteristic of the modern barter is that the trade uses barter currency or barter credit, which can be used as money, but only used on the barter platform, i.e., barter trade does not use money. Therefore, the barter pool is a relatively closed economy, which can maintain a general profit for each firm on the barter platform. For example, the barter price is the same as the market price.