Computer Science

When individuals in a social network learn about an unknown state from private signals and neighbors’ actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their aggregative efficiency index. Networks where agents observe multiple neighbors but not their common predecessors confound information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

Many social network phenomena such as norms and cascades depend not only on what agents believe but on what they believe other agents believe.   One important instantiation of agents’ beliefs about beliefs is knowledge commonly known by all agents.  However, current definitions that capture this idea such as common knowledge and common belief are too restrictive for use in understanding strategic coordination and cooperation in social network settings. In this talk, I will propose a relaxation of common belief called factional belief that is suitable for the analysis of social network phenomena.  I will then show how this definition can be used to analyze revolt games on sparse graphs.  In particular, I will show that for a certain natural class of revolt games, the degree sequence of a network almost entirely characterizes whether any equilibrium can often support a large revolt.  The proof is via an efficient algorithm for determining the same.  A key goal of this talk is to provide the background to start a conversation about where common knowledge (or its variants) can help us to reason about social network phenomena.

We characterize the optimal communication network in a firm with a modular production function, which we model as a network of decisions with a non-overlapping community structure. Optimal communication is characterized by two hierarchies that determine whom each agent receives information from and sends information to. Receiver rank depends only on module cohesion while sender rank also depends on decision-specific values of adaptation. When the hierarchies are the reverse of each other, optimal communication is bottom up in aggregate, and when they are the same, it has a core-periphery structure, in which the core contains the most cohesive modules.

Other peoples' experiences serve as primary sources of information about the potential payoffs to various available opportunities. Homophily in social networks affects both the quality and diversity of information to which people have access.On the one hand, homophily provides higher quality information since observing the experiences of another person is more informative as that person is more similar to the decision maker. On the other hand, homophily lowers the variety of actions about which people can learn when a group ends up herding on specific actions about which they have better information. This can lead to inefficiencies and inequalities across groups, as we show. Homophily lowers efficiency and increases inequality in sparse networks, while enhancing efficiency and decreasing inequality in denser networks. We characterize conditions under which groups herd on separate actions, and show how such homophily-induced herding driven by limited scope of information differs from standard forms of herding driven by cascading inferences.

We introduce a model of strategic experimentation on social networks where forward-looking agents learn from their own and neighbors’ successes. In equilibrium, private discovery is followed by social diffusion. Social learning crowds out own experimentation, so total information decreases with network density; we determine density thresholds below which agents asymptotically learn the state. In contrast, agent welfare is single-peaked in network density, and achieves a second-best benchmark level at intermediate levels that achieve a balance between discovery and diffusion. We also study how learning and welfare differ across directed, undirected and clustered networks.

When a user shares her data with online platforms, she reveals information about others in her social network. In such a setting, network externalities depress the price of data because once a user's information is leaked by others, she has less reason to protect her data and privacy. These depressed prices lead to excessive data sharing. We characterize conditions under which shutting down data markets improves welfare. Platform competition does not redress the problem of excessively low data prices and too much data sharing and may further reduce welfare. We propose a scheme based on mediated data sharing that improves efficiency.

Dynamic network data have become ubiquitous in social network analysis, with new information becoming available that captures when friendships form, when corporate transactions happen and when countries interact with each other. Moreover, data are available about individual actors in the network, including information about the spread of viral (disease or otherwise) processes between individuals in the network. We argue that the dynamics of these processes should be coupled with those of the network evolution in order to improve downstream inference and develop experimental and observational studies --- we do so by studying a class of stochastic epidemic models that are represented by a continuous-time Markov chain such that disease transmission is constrained by the contact network structure, and network evolution is in turn influenced by individual disease statuses. When aiming at estimating causal effect we couple this dynamic modeling with a study of the violation of classical no-interference assumptions, meaning that the treatment of one individuals might affect the outcomes of another. To make interference tractable, we consider a known network that describes how interference may travel. We discuss two settings: (1) design of experiments under known network interference and (2) an observational setting where the radius (and intensity) of the interference experienced by a unit is unknown and can depend on different sub-networks of those treated and untreated that are connected to this unit. In the former we propose an efficient design that leads to the naive difference in means estimator being consistent while in the second we show that under mild regularity conditions, an inverse weighted estimator is consistent, asymptotically normal and unbiased for the average treatment effect on the treated.

We consider a setting where agents in a social network take binary actions that exhibit local strategic complementarities. Their payoffs are affine and increasing in an underlying real-valued state of the world. An information designer commits to a signaling mechanism that publicly reveals a signal that is potentially informative about the state. She wants to maximize the expected number of agents who take action 1. We study the structure and design of optimal public signaling mechanisms. The designer’s payoff is an increasing step function of the posterior mean (of the state) induced by the realization of her signal. We provide a convex optimization formulation and an algorithm that obtain an optimal public signaling mechanism whenever the designer’s payoff admits this structure. This structure is prevalent, making our formulation and results useful well beyond persuasion in networks. In our problem, the step function is characterized in terms of the cores of the underlying network. The optimal mechanism is based on a “double-interval partition” of the set of states: it associates up to two subintervals of the set of states with each core, and when the state realization belongs to the interval(s) associated with a core, the mechanism publicly reveals this fact. In turn, this induces the agents in the relevant core to take action 1. We also provide a framework for obtaining asymptotically optimal public signaling mechanisms for a class of random networks. Our approach uses only the limiting degree distribution information, thereby making it useful even when the network structure is not fully known. Finally, we explore which networks are more amenable to persuasion, and show that more assortative connection structures lead to larger payoffs for the designer. On the other hand, the dependence of the designer’s payoff on the agents’ degrees can be quite counterintuitive. In particular, we focus on networks sampled uniformly at random from the set of all networks consistent with a degree sequence, and illustrate that when the degrees of some nodes increase, this can reduce the designer’s expected payoff, despite an increase in the extent of (positive) network externalities.

Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked because the goods are substitutes or complements in consumption. We study how changes in producers' costs pass through to two key outcomes: prices and welfare. We consider the positive question of which cost changes (e.g., shocks to commodity prices) are most amplified by strategic behavior. We also investigate the policy question of which marginal taxes and subsidies are best for welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of principal components in the goods space, independent in the sense that a cost change incident on any component passes through to the price only of that component. Pass-through coefficients are determined by associated eigenvalues of a demand matrix and yield an ordering of principal components. The ordered basis permits a simple cutoff characterization of optimal tax-and-subsidy interventions, which subsidizes principal components, with high pass-through, and taxes ones with low pass-through. The gain in welfare achievable by an optimal tax scheme is increasing in a suitable measure of eigenvalue dispersion. The results permit us to leverage the theory of spectral approximation to design optimal interventions even when the demand system is observed with a lot of noise.