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.

We study when interventions can robustly increase market surplus despite imprecise information about economic primitives, in a setting with many strategic firms possessing market power. The key sufficient condition, recoverable structure, requires large-scale product complementarities. The analysis works by decomposing the incidence of interventions in terms of principal components of a Slutsky matrix. Under recoverable structure, a noisy signal of this matrix reveals enough about these principal components to design robust interventions. Our results demonstrate the utility of spectral methods for analyzing imperfectly observed strategic interactions with many agents.

We study network games in which players choose partners and an effort level. There is a finite set of players N, each choosing an action si; from an ordered set Si and forming links G, with payoffs ui(G, s). We study two stability concepts: an outcome (G, s) is strictly pairwise stable if (i) actions s are a Nash equilibrium for fixed G; (ii) no player wishes to unilaterally sever an existing link; and (iii) no pair of unlinked players both weakly desire to form a link. The network is strictly pairwise Nash stable if no player can strictly benefit from simultaneously changing their action and severing some links.

Standard game-theoretic analysis yields highly incomplete descriptions of behavior in complex games of complete information. A key part of the reason is that standard models do not account for the role of complexity in shaping players' strategic behavior. We investigate the implications of complexity empirically and theoretically, focusing on the game of chess---a good setting for our study because it is a rare example of an extensive-form game that is played by experienced, motivated players, and for which we have vast amounts of data.

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.

For a large organization to successfully complete a complex project, many constituent tasks must all be successfully completed. A typical such task can be completed only if several other, tailored input tasks are completed. Thus a complex project, such as designing a new product and bringing it to market, requires many collaborations among workers to succeed, both within and across business units. Some collaborations succeed, while others fail. Corporate culture---a broad notion that entails many aspects of the working environment---supports collaborations by establishing norms and reducing miscommunications or misunderstandings. However, the strength of a corporate culture is endogneous. Individual actions of workers that run counter to it undermine it and adhering to the corporate culture in a given situation can be costly to a worker. Because a strong corporate culture relies on costly, voluntary investments by many workers, we model it as an organizational public good, subject to standard free-riding problems, which become severe in large organizations. Indeed, a standard analysis would suggest that workers' incentives to make voluntary contributions to the corporate culture vanish as an organization becomes large, because their marginal impact becomes negligible while their marginal cost does not. This raises an important question: Why do workers exert voluntary effort to enhance the corporate cultures of large organizations? We propose a perspective on this question based on a network model of complex production within a large organization: The productive activity of the organization occurs via the completion of tasks, where a given worker in charge of a task relies on the completion of several types of essential subtasks, which are incorporated into the task via collaborations with other workers. We find that voluntary contributions to culture can be sustained, because an organization's equilibrium productivity is endogenously highly sensitive to individual contributions. This implies a new mechanism generating incentives for voluntary, decentralized investment in culture even as an organization becomes large and the free-rider problem becomes severe: the marginal impact of contributions becomes large enough to compensate. However, the completion of complex tasks is then necessarily fragile to small shocks that can disrupt the organization's culture, such as a merger or a change in the company's top management.

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.

An economy can be thought of as a network in which the nodes are agents and links among them represent heterogeneous opportunities for exchange or cooperation. This paper argues that studying properties of such a network -- how dense it is, how "central" various agents are in it -- yields insights about issues such as the efficiency and fragility of an economic system, as well as its market outcomes. We develop this conceptual point in a model of a public goods economy: one in which each agent can incur a private cost to take an action -- e.g., reducing pollution -- that creates nonrival but heterogeneous benefits for others. The network we study is a directed, weighted graph in which an edge from agent i to agent j captures the marginal benefits i can provide to j, at the current action profile, as i increases his public good provision.