The recent growth in large-scale networks and online communication has generated new ways in which networks can diffuse information. But a number of research questions remain unanswered, such as how networks affect innovation and how network structure shapes competition among ideas or technologies.
The goal of the research is to examine how research communities and links between them affect innovation. It develops a theory of how connections and absences of connections among individuals influence the process of innovation, with particular attention paid to the role of "boundary agents" who straddle different communities.
Intellectual Merit. The project is poised at the frontier of computer science and economics. Computer scientists have long studied how information is created and processed. Economists have long studied incentives for innovation. This project introduces a new paradigm. It studies innovation in networks of people and firms, where information flows through network links. Developing this paradigm requires a deep understanding of the graph-theoretic properties of the network and the incentives of the participants. The combined tools of the principal investigators represent a significant methodological advance not only for computer science and economics, but the sciences more generally.
Broader Impact. The project increases participation of women and under-represented groups in science. A graduate course trains students in state-of-the-art tools in network science from all relevant fields including economics, social sciences, mathematics, and computer science, while under graduate courses incorporate social network examples. In addition, the research advances understanding about the participation of underrepresented groups in social and economic networks. Finally, the scientific aims of the project develop knowledge that can inform policy makers in designing incentives for innovation, discovery, and diversity.
How do networks affect innovation? How does network structure shape competition among ideas, or technologies? What policies might influence innovation and diffusion to achieve economic or social goals? These are timely and pressing questions, given the recent growth of large-scale networks and on-line communication. The first model considers agents whose benefits derive from the average of his neighbors' contributions, rather than the sum of his neighbors' contributions. This model would correspond to a peer effect model common in labor economics. Previous results on public goods contributions games would not apply to this case, as the underlying payoff matrix is not symmetric. The result in this case is that the payoff matrix can be normalized as a vector of 'fixed effects' times a symmetric adjacency matrix. This adjacency matrix is a stochastic matrix, and, thus the spectral radius is less than one. This leads directly to the finding that all agents make some contribution to public goods (i.e., there is always an interior solution). And these contributions relate to agents' Bonacich centrality measures in the normalized adjacency matrix. A second model makes a major departure from previous work by considering agents' preferences for social status within their social environments. Building on social psychology, the model assumes that agents benefit from the overall provision of public goods, but they also like to be the major contributors among their friends. This assumption gives a new reason for agents to provide public goods (a status motive) but it can also lead to underprovision of public goods (there is also a discouragement effect). The equilibria of this game display several interesting properties. First, in any equilibrium profile, there are only two levels of contributions, one higher than the other. Equilibria then consists of 'major contributors,' who adopt the high contribution level, and 'minor contributors,' who adopt the low contribution level. Second, we can precisely define the size of the neighborhoods that support high effort levels. The neighborhood is bounded and is decreasing in the importance that individual agents place on status. That is, the more agents' care about status, only agents in smaller neighborhoods will make high levels of contributions. This is the 'discouragement effect' from not being the top contributor. Finally, a pure equilibrium exists, since the cut between major contributors and minor contributors is a potential function. This result directly relates the analytical solutions to a strategic game on a network to a well-known graph theoretic concepts. The third model focuses on status concerns. We construct a model where agents loss status when they produce/consume a quantity of goods that is lower than the friends and neighbors. The model captures the essence of conspicuous consumption and the phenomenon of "keeping up with the Jones." In this model we have several findings. The equilibrium set is a complete lattice, with a highest consumption equilibrium vector and a lowest consumption equilibrium. We conduct comparative statics to show that the equilibrium levels of consumption are increasing in agents’ preferences for consumption and their preferences for status. The comparative statics on the links structure are more difficult, yet we nonetheless obtain some interesting results. We show that high levels of consumption can only be sustained when subsets of agents are sufficiently "cohesive." By cohesive we mean that large proportions of agents’ neighbors are contained in the same subset. When subsets are "cohesive," agents compare their production/consumption to a greater proportion of agents, and hence it is possible to have higher equilibrium levels of consumption.
