Information Demand and Dynamic Contests

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This project in economic theory consists of two parts: information demand and dynamic contests. The first is reasonably well developed while the second is in its early stages. Also included is a discussion of an ongoing but much better focused project on bargaining theory, appealing to an established psychological fact that individuals' behavior is largely governed by their aspirations.The first two subprojects are part of a greater agenda to understand the most basic questions about the nature of information demand, namely, does the so-called Law of Demand hold? Well-known counterexamples in static environments suggest not. In fact, we find two separate contexts where it does hold, one extremely relevant in applied contexts. In the most advanced sub-project, we find that if information is very cheap, and thus demand very large, then the law of demand is eventually true. Additionally, in this context, we show that the fundamental insight provided by Blackwell's Theorem largely does not matter. In fact, when one is permitted to acquire a large enough number of independently and identically distributed copies of any given signal, then a complete ordering over experiments/signals arises. That two signals are not sufficient for each other in a statistical sense is no longer relevant. What matters is an asymptotic measure of sufficiency. We extend this so far as to deduce a very simple logarithmic formula for the demand for information, when prices are low enough.This part of the work should make methodological and substantive contributions to Bayesian decision theory and game theory. For Bayesian decision theory, the centrality of the information demand question is manifest. But the methods introduced from asymptotic theory should prove extremely tractable and basic tools for theorists considering information in the future. Economists' traditional narrow focus on an overly stylized of model of one-shot information purchase (today I buy my signal, tomorrow I act) likely owes its roots to Blackwell's Theorem. In some sense, the law of large demand paper starts from a different yet contemporaneous foundation (work by Chernoff).The third project is less developed, being still at an early stage. It proposes a new mechanism design question, namely what is the optimal design of a dynamic contest, as a function of the payoff' and signaling structure? The wide range of cited instances of such contests, from sports to employment arrangements to television game shows, speaks to the importance of understanding this micro market structure. We have formulated this in continuous time, and have proposed some basic features of the nature of the contest design. This work is intended as a first effort on an unconsidered problem that is incredibly generic. The substantive value of such work is hopefully clear. Many of the technical hurdles are as yet unknown.