We define a hypergraph by a set of associations which consist of nonexclusive two or more players. It is a generalization of a graph (or a network) in the sense that an association, the counterpart of a link in a hypergraph, connects any number of nodes, not simply a pair of nodes. We...

We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts–Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing,...

We consider the dynamic network formation problem under the requirement that the whole network be connected and remain connected after q nodes are destroyed. We propose the concept of dynamic Cq-stability and characterize dynamic Cq-stable networks for any qÏ0. Comparison with the outcome in...

We model a hierarchy consisting of possibly corrupted agents who process information, and consider the problem of designing the efficient hierarchy structure and configuring the agents who differ in their honesty. If the only role of agents is to report the information to their direct superior,...

In this paper, we consider the network as an alternative communication channel to undirected advertising in the market. The main distinctive feature of the network-embedded transaction is the interdependency of buyers' purchasing behavior. Since most transactions in a network are made...

We introduce a new notion of connectivity, what we call weak connectivity, in a directed network where communication is one-way, and show that weak connectivity is equivalent to the usual concept of connectivity if the outdegree of each node is at most one, referred as the [DC] condition. Based...

In this paper, we consider the network as an alternative trading environment to the market. The main distinctive feature of the network transaction is the dependence of buyers' purchasing behavior, which makes all consumers not equally valuable to a seller. We characterize the optimal behavior...