The Value of Information in Strategic Environments

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Project Abstract Information is a key input into production in today's economy. Some believe that the world's economy is undergoing an information revolution that will have as large an impact as the industrial revolution of two hundred years ago. A basic research area for economists in the information age is to understand why and how information is valuable. There is a well developed theory (dating back to the 1950's) of the value of information in single person decision problems under uncertainty. It was shown that information is valuable in every decision problem exactly if it is more informative in a natural statistical sense. In single person decision problems, more information is always better. But the economy is strategic. We cannot analyze each decision maker in isolation. Rather, we need to understand how each participant in the economy will behave, taking into account how he or she thinks others will behave. The value of information in strategic settings is a much more complicated problem. More information can sometimes make everyone worse off. For example, insurance markets make profits for insurance companies and make consumers better off by reducing risk. If the consumers had access to more information, the insurance markets would shut down and everyone would be worse off. The purpose of this project is to develop a theory of the value of information in strategic settings. Four sets of questions will be addressed. The first three are more technical but provide the framework to think about these issues. First, what is a necessary and sufficient condition for one information system to be more valuable than another in all strategic settings? The condition will be extremely strong, but provides an important benchmark. Second, what is a necessary and sufficient condition for two information systems to be almost as valuable as each other in all strategic settings. Third, for exactly which classes of strategic situations do more informative information systems make every agent better off? And for which classes of strategic situations do more informative information systems make every agent worse off? The fourth component is more applied. An important type of strategic problem is a coordination game: a group of firms would like to coordinate their actions, but they may disagree on which action they should coordinate. An example would be software companies choosing standardized protocols. This project develops a theory of the value of information for coordination games. Existing work shows the importance of common knowledge in achieving co-ordination. It is important not only what each firm knows, but also what they know about what other firms know, and so on. Thus the ability of an information system to generate approximate common knowledge will be a key determinant of the value of information. This is an important observation because highly distributed information systems, such as the internet, are especially poor at generating approximate common knowledge.