Network Seeding with Local Network Effects

This talk is based on a model of network effects that are "local". That is, rather than being influenced by choices made across the entire network or population, each agent is influenced by a (typically small) subset of other agents, this subset varies across agents, and naturally, agents have more information about their own subset (or "neighborhood") than they do about those of others. Outcomes in a setting of this kind thus depend on the structure of an underlying social, business or technological network, which is the graph created by these local connections.

Firms and policy makers can influence outcomes by "seeding" this network: that is, inducing adoption using a subsidy (for instance, by giving a product away for free) for a subset of agents connected by the underlying network. The optimal seeding of a network has a wide variety of applications. These include profitably launching a product that displays network effects, building awareness about a product or topic using network-based marketing, optimizing the performance of a technology based on a peer-to-peer network, and igniting collaborative innovation or R&D within an organization or a specific geographic region. Seeding can either be targeted, based on knowledge the external entity has about the connectedness or network position of an agent, or can be random.

In general, the optimal seeding of a network can be described as a model with three stages: first, an external entity (a firm or policy maker) chooses a seeding strategy; next, depending on the seeding strategy, a subset of (and perhaps all) the agents connected by the underlying network play a game in which they each choose a (possibly costly) action, and finally, the external entity and the agents receive their payoffs, which may depend on the seeding strategy chosen by the external entity, the actions chosen by the other agents, and the structure of the underlying network.

In this talk, I will describe two sets of results. The first set relate to modeling network games of the kind described in stage two above when agents have perfect local information but incomplete global information about the structure of the underlying social network. I characterize the properties of all pure-strategy Bayes-Nash equilibria of a fairly general class of such games, showing that they are all in threshold strategies, that they can be strictly ranked based on total surplus, and that the greatest such equilibrium is uniquely coalition proof. I also show an equivalence between the equilibria of these network games and the solutions based on a widely used idea of "fulfilled" or rational expectations equilibrium.

I apply these results to characterize a model of optimal seeding of its consumers by a firm for a product that displays local network effects. First, I show that random seeding is almost always optimal if the firm does not know each agent’s connectedness or network position. I then analyze how the structure of the network or the distribution of graphs that it is drawn from affects the optimal targeted seeding strategy. I provide a set of such conditions which lead to a simple and intuitive optimal seeding strategy that involves "seeding the fringes rather than the hubs". I will also discuss how relaxing these assumptions is likely to change the optimal seeding strategy, and outline preliminary results that characterize optimal seeding when technology adoption is determined by dynamic "myopic best-response" model of diffusion on the social network.

See this background paper for more information.