The science of social networks is a central field of sociological study, a major application of random graph theory, and an emerging area of study by economists, statistical physicists and computer scientists. While these literatures are (slowly) becoming aware of each other, and on occasion drawing from one another, they are still largely distinct in their methods, interests, and goals. Here, my aim is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks and the two major types of models: those based on random graphs and those based on game theoretic reasoning. I highlight some of the strengths, weaknesses, and potential synergies between these two network modeling approaches.

We analyze a model of diffusion on social networks. Agents are connected according to an undirected graph (the network) and choose one of two actions (e.g., either to adopt a new behavior or technology or not to adopt it). The return to each of the actions depends on how many neighbors an agent has, which actions the agent’s neighbors choose, and some agent-specific cost and benefit parameters. At the outset, a small portion of the population is randomly selected to adopt the behavior. We analyze whether the behavior spreads to a larger portion of the population. We show that there is a threshold where “tipping” occurs: if a large enough initial group is selected then the behavior grows and spreads to a significant portion of the population, while otherwise the behavior collapses so that no one in the population chooses to adopt the behavior. We characterize the tipping threshold and the eventual portion that adopts if the threshold is surpassed. We also show how the threshold and adoption rate depend on the network structure. Applications of the techniques introduced in this paper include marketing, epidemiology, technological transfers, and information transmission, among others.

Abstract: A brief introduction and overview of models of the formation of networks is given, with a focus is on two types of models. The …rst views networks as arising stochastically, and uses random graph theory; while the second views the links in a network as social or economic relationships that are chosen by the involved parties, and uses game theoretic reasoning.

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from “information hubs”, which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication may not always be a best response, it is an equilibrium when the communication network induces asymptotic learning. Moreover, we contrast equilibrium behavior with a socially optimal strategy profile, i.e., a profile that maximizes aggregate welfare. We show that when the network induces asymptotic learning, equilibrium behavior

Preliminary version Ranking systems are becoming increasingly important in many areas, in the Web environment and academic life for instance. Presumably a ranking helps individuals to make decisions by providing them with relevant information. In a world with a tremendous amount of choices, a ranking plays also the crucial role of influencing the attention that is devoted to the various alternatives. In recurrent situations, attention will, in turn, alter the new statements on which subsequent rankings will be based. The paper proposes an analysis of this feedback by studying some reasonable dynamics that a ranking method may induce. The feedback is shown to depend strongly on the used ranking method. Two main families of methods are investigated, one based on the notion of ’handicaps’, the other one on the notion of peers ’ rankings.

The paper proposes a model to study the conditions under which complex networks emerge (or not) when agents are involved in a dynamic coordination setup. In contrast with existing literature, however, our main focus is not on the entailed issue of equilibrium selection. Instead, our aim is to shed light on how agents’e¤orts to coordinate a¤ect the process of network formation in a large and complex environment. The model posits that, over time, new links are created if they are pro…table, and existing links disappear due to exogenous decay. Alongside this struggle between link creation and link destruction, agents’choices in the coordination game adapt to their current local conditions and thus coevolve with the social network. We characterize analytically the long-run behavior of the system and show that, as a function of the underlying parameters, the process displays sharp (discontinuous) transitions, resilient network transformations, and equilibrium multiplicity. As it turns out, these are features observed in a wide number of network phenomena in social environments.