Performance incentives tied to joint outcomes — such as equity for startup executives or bonuses for marketing teams — are a common tool for motivating teams. How should such incentive schemes be designed and how should they take into account the team's production function? We examine these questions in a simple non-parametric model of a team working on a joint project. Each member of the team chooses a costly effort level. These actions jointly determine a real-valued team performance according to a sufficiently smooth, increasing function of the efforts, which may entail interactions such as complementarities among agents' efforts. Any performance level determines a probability distribution over observable project outcomes.

Prediction problems are ubiquitous in the economy. To give a few examples, firms selling products often want to predict customers' willingness to pay and may use business analytics tools to do so. In science and engineering, researchers want to predict the viability of compounds in domains ranging from drug discovery to materials science. Campaigns and observers want to predict elections, and may commission polls to do so.

In recent years, viral content on social media platforms has become a major source of news and information for many people. Which stories go viral is jointly determined by the algorithms generating platform news feeds and users' actions on the platforms. We study this process with an equilibrium model of users interacting with shared news stories, focusing on how the design of news feeds affects how users learn. In our model, rational users arrive sequentially, observe an original story (i.e., a private signal) and a sample of predecessors' stories in a news feed, and then decide which stories to share. The observed sample of stories depends on what predecessors share as well as the sampling algorithm generating news feeds.

Equity compensation is widely used to motivate members of a team, such as a startup, to work toward a common goal. A natural question, about which little is known, is how the structure of collaborations should influence the design of equity compensation. We analyze this problem in a standard quadratic-payoffs network game model of production with heterogeneous complementarities. Each member of the team chooses a level of costly effort. This effort makes a "standalone" contribution to the firm's output, but there are also production complementarities: some pairs of workers generate an output proportional to the product of their efforts. In our model, the pattern of these complementarities is exogenously given and defines a network.

In social-learning settings where individuals receive private signals and observe network neighbors' actions, the network structure often obstructs information aggregation. We consider sequential social learning with rational agents and Gaussian signals and ask how the efficiency of signal aggregation changes with the network. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This leads to a detailed ranking of networks for social learning 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.

We conduct a sequential social-learning experiment where subjects take turns guessing a hidden state based on private signals and the guesses of a subset of their predecessors. A network determines the observable predecessors, and we compare subjects' accuracy on sparse and dense networks. Accuracy gains from social learning are twice as large on sparse networks compared to dense networks. Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the finding is difficult to reconcile with rational-learning models.

Agents learn about a changing state using private signals and their neighbors' past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbors' estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioral assumption. We examine whether information aggregation is nearly optimal as neighborhoods grow large. A key condition for this is signal diversity: each individual's neighbors have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity---e.g., if private signals are i.i.d.---learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one's signal quality than to one's number of neighbors, in contrast to standard models with exogenous updating rules.