Stabilizing the network in presence of agents using flow graph and Shapely value in B2B E-commerce Samara Mubeen Department of Information Science and Engineering J.N.N.college of Engineering, Shimoga, Karnataka, India Dr. K.N.Subramanya Department of Industrial engineering and Management R.V.College of Engineering, Bangalore, Karnataka, India Abstract- B2B e-commerce is widely spread. One of problems is to identify the supplier who will manufacture sub product and send back to manufacturer for assembling it into a final product. After identifying the best supplier we want to transfer the information about the sub product to the supplier and supplier should respond to this via the agents. We are going to use a flow graph for designing the network having the supplier and manufacture and use Shapely value to check whether an exact sub product order by manufacture is reaches the back to the manufacture after manufacturing at the suppliers. Keywords – Flow graph, Shapely value, B2B e-commerce. Agent. I. INTRODUCTION As competition from emerging economies puts pressure on global supply chains and as a new constraint emerges, it presents opportunities for new approaches such as the game theory approach to solving the transshipment problem. Recent real world examples of these principles illustrate how organizations have leveraged these ideas for competitive advantage. Dell Computer Corporation was able to overcome the strategic constraints of the bullwhip effect of increasing demand variation and forecast error in the upstream supply chain faced by the other PC manufacturers. . In computer science graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. For instance, the link structure of a website can be represented by a directed graph, in which the vertices represent web pages and directed edges represent links from one page to another. A similar approach can be taken to problems in travel, biology, computer chip design and many other fields. The development of algorithms to handle graphs is therefore of major interest in computer science. The transformation of graphs has been often of major interest in computer science. The transformation of graphs has been often formalized and represented by graph rewrite systems. Complementary to graph transformation system focus on rule based in- memory manipulation of graphs are graph database geared towards transaction safe, persistent storing and querying of graph structured data. A flow is a way of sending objects from one place to another in a network. The objects that travel or flows through the network are called flow units or units. For example, flow units can be a commodity, finished goods, or information. The network is presented as a graph with a set V whose elements are called vertices, and a set A of pairs of vertices called edges. The graph is denoted G = (V,A). In practice, we specify a flow as a directed graph. The vertices in a directed graph are commonly called nodes, and the directed edges are often called arcs. The nodes from which units enter through a network are called source nodes, and the nodes to which the flow units are routed to be called sink nodes. Source nodes offer supply, which is represented by the number of units available at the node. Sink nodes usually have demand, which is represented by the number of units that must be routed to them. A Introduction to game theory International Journal of Innovations in Engineering and Technology (IJIET) Vol. 4 Issue 1 June 2014 243 ISSN: 2319 – 1058