Maximizing Cascade of Innovation on Networks

Abstract

D iffusion of innovation is usually difficult, because many members in society had not adopted innovation initially and people are usually rational: they select risk dominant solution and keep initial state. Cascade phenomena, which are sequences of adoption by agents, are the important driven forces for the society to make a successful diffusion of innovation, emergence of social norm and opinion formation. There are certain kinds of networks (ex. social network) under these cascade phenomena and the topologies will affect the dynamics. The cascade phenomena can occur in specified range of conditions (or known as cascade windows) defined by both the average degree of the underlying network topologies and the threshold of each agents (or nodes). This paper shows what kind of network topology maximizes cascade of innovation in terms of cascade window using evolutionary optimization method and how the network topology drives cascade phenomena at wider conditions than other networks. From results of the optimization, the best networks have both cluster of hub nodes and cluster of nodes with a few links, which are called vulnerable nodes. By a detailed consideration of topologies of the best networks, the authors also propose a network model (P model) to maximize the cascade of innovation, in which a mechanism of probabilistic growing network is used. At each discrete time step, one new node and constant number of new links are introduced and added to hub nodes or vulnerable nodes in the network depending on a certain probability. The P model has better scalability compared with evolutionary optimizing method in terms of time complexity and can make networks that drive cascade phenomena at wider conditions than evolutionary optimized networks. The success of P model strengthens the importance of both cluster of hub nodes and cluster of vulnerable nodes for maximizing cascade of innovation on networks.