Collaborative Research: A Global Theory of Information and its Nonconcavity, with Economics and Social Applications

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This project utilizes new tools to develop a tractable theory of information, and then applies it in two decision-theoretic and equilibrium settings. In addition to the theory, the study offers new insights into diverse research areas such as finance, social dynamics and structure, and social networks. There are both theoretical and applied components of this study in the area of social dynamics and structure. The purely theoretical component develops a general theory of the non-concavity of the value of information, when measured in its natural units of sample size. Unlike prior work on the static value of information, this new theory derives the entire schedule of the marginal value of information. Starting with a new model of variable quantity information, the first methods employed for option pricing are used to solve the problem. The applied theory component of the study offers two new insights. First, social change may be punctuated and sudden. In this sense, the non-concavity is a major agent of change. While developed for a static setting, it applies dynamically, leading society only periodically to reevaluate the wisdom of its choices. This forces punctuated social change, where so-called (S,s) rules arise without any fixed costs, and thus small causes can have big effects.Second, the collection of information at the individual level fosters the exchange of information with neighbors, creating a scope for multiple equilibria and coordination failures in the social production of information. In a word, convexity creates a complementarity that encourages multiple equilibria. Ignoring this dimension, the design of labor markets, urban planning, career counseling, and anti-segregation policies might be grossly misguided. The results illustrate the potentially harmful role of mass media in curbing the incentives for decentralized information collection and exchange, and for promoting local uniformity in social behavior.The broader and long-run impacts of this project are far-ranging. For example, increasing returns inherent in the demand for information creates the potential for a generic market failure. In addition, the exchange of information is arguably the main purpose of social networking. Informational networks increasingly appear to play a major role in shaping key social phenomena, such as the diffusion or clustering of employment opportunities, voting patterns, and financial investment attitudes. This project is the first ever to explore the social implications of the fundamental non-concavity in the value of information.The educational impact of this study would spans multiple fields. The development of a tractable, transparent, yet rigorous benchmark model of information provides a tool to illustrate and teach these phenomena in fields where the demand and exchange of information play a central role, such as sociology, public health, telecommunication policy, and education. It enables researchers from these different fields to establish a common ground and vocabulary, and fosters inter-disciplinary work. The insights that information can be usefully measured and that it initially may well have increasing returns, has broader impact for many fields studying informed human behavior--from sociology to psychology. This research also informs optimal policy towards research and development. Furthermore, the analysis of the informational foundations for punctuated social change provides a useful informational tool for those studying the history of science through Thomas Kuhn's paradigm in his (1962) "Structure of Scientific Revolutions."