Microeconomic Theory
Applied Microeconomics
Psychology and Economics

Microeconomic Theory
International Trade
Undergraduate Macroeconomics
Undergraduate Econometrics

May 1998 (Oral) Microeconomic Theory and International Economics
May, 1997 (Written) Microeconomic and Macroeconomic Theory

Release of Information with Imperfect Memory and Other Essays

Professor Benjamin Polak
Professor David Pearce
Professor Stephen Morris

May 2001

M.Phil. (economics), 1998, Yale University
M.A. (economics), 1997, Yale University
B.A. (with honors in economics and mathematics), 1996, Grinnell College

Graduate Student Fellowship, Cowles Foundation, Summer 2000
Carl A. Anderson Dissertation Fellowship, Cowles Foundation, Fall 1999
Yale University Fellowship, Fall 1996 – Spring 1999
Meritorious. Mathematical Contest in Modeling, sponsored by COMAP, Spring 1994

Teaching Assistant, Introductory Microeconomics, Yale University, Fall 2000
Teaching Assistant, Introductory Macroeconomics, Yale University, Fall 1998, Spring 1999, Spring 2000

"What Have You Done For Me Lately? Release of Information and Strategic Manipulation of Memories."

"Revising Non-Additive Priors" (joint with Ricky Lam).

"Recipient Needs, US Interests and UN General Assembly Votes in Foreign Aid Allocation Decisions."

In a wide range of economic interactions, agents are rewarded at some critical date on the basis of an assessment of their past performance. In many such cases, an objective criterion that summarizes past performance is not available and, as a result, assessors have to rely on their memories of past informative events. The main chapter of my dissertation takes a bounded-rationality stance, assuming that imperfect memory is an indisputable limitation of human cognition. Using assumptions directly based on recent findings from cognitive psychology, I build a formal model of memory and then explore its economic consequences by addressing the issue of how one should time a sequence of informative events in order to manipulate the memories of one's forgetful assessor.

The general framework is relevant to almost any social or economic setting where products or people undergo periodic assessment. The results can be applied to executives managing news prior to an IPO, to advisors managing political campaigns, to advertisers scheduling the airing of commercial spots prior to a product or movie release, to employees timing their efforts prior to a promotion decision, and to students timing their class contributions prior to the end of term. An application particularly close to home is the timing of publications and seminars by junior faculty prior to a tenure decision or by a graduate student prior to the job market.

In modeling the memory technology, I invoke an array of experimental evidence, which shows that memory operates on the principles of similarity (cue dependence) and repetition (rehearsal). Loosely, cue dependence refers to the phenomenon that current events trigger memories of similar past events, and rehearsal refers to the fact that recalling the memory of an event makes it more likely to be remembered in the future.

To see how cue dependence and rehearsal matter for the problem of releasing information, assume that an incumbent senator faces re-election at some future date. Public support for the senator depends on the electorate's memories of past events pertaining to the senator, such as what side he took in a controversial dispute, or how he handled a labor union crisis. Suppose now, that a few months before the election, our senator is lucky enough to get a series of positive boosts to his image from a number of recent events. Now, he has to schedule the announcement of a new popular tax plan and a public appearance that will generate a lot of positive publicity. You have just been hired as his political consultant. How do you advise him? On the one hand, since people forget, it is wise to time these two events as late as possible in order to make them more memorable at the time of the election. I refer to this as the recency effect. On the other hand, you want these events to reinforce the existing good memories of past events. To maximize this rehearsal effect, the two events should be scheduled as early as possible, to reinforce the "good news", before these memories fade away. Optimal decisions are dictated by this trade off between the recency and the rehearsal effects.

I find that, as this sketch suggests, the timing of events is crucial for what the assessors remember. In quasi-rational models, it is often the case that the order of informative signals is important, since it determines how people will perceive future events. In this model, what is important is not only the order (i.e., which event comes first and which comes second), but the actual spacing (i.e., the amount of time that elapses between the two events). The shorter the amount of time between two events the more effective will the second one be in triggering the memory of the first. This logic dictates that successes should be bunched together in order to reinforce each other's memories and, by the same token, failures should be spread apart. In addition, I show that the optimal rule for when to release information has a nice simple form. Loosely speaking, we can think of a streak of stochastic events (both good or bad) creating a "stock" of news. When this stock is above a certain threshold level, it triggers the agent to try to generate further successes. These successes not only reinforce fresh memories of past successes, but also guarantee that past failures will not be reinforced.

This paper belongs to the vein of economic literature that injects psychological insights on human behavior and cognition into existing economic models, in an attempt to improve their descriptive power. Sendhil Mullainathan was the first to incorporate memory imperfections into economics. His goal was to show how an agent’s own memory imperfections can explain often-observed decision making biases. What differentiates my paper from Mullainathan’s, as well as from most of the existing literature in behavioral economics, is my investigation of the strategic considerations of bounded rationality. Such considerations arise when a fully rational agent recognizes a cognitive limitation or bias from which others suffer, and he now faces the problem of how to modify his actions in order to manipulate it for his own benefit. In my paper, for example, the senator recognizes the electorate’s memory imperfections, and he times a sequence of events in an effort to manipulate the memories that the electorate will have at election time.

In a separate paper, I am working to extend the model just described, to include the game- theoretic interaction that arises when two agents are competing in front of a common assessor. In a presidential race, for example, two or more candidates compete for support from the electorate, and in releasing informative events each candidate has to keep track of not only his past record, but the past record of his opponents as well.

My third paper is called "Revising Non-Additive Priors", and is joint with Ricky Lam. Recent work in decision theory models subjective beliefs by a capacity, which is essentially a non-additive probability measure. Such beliefs capture the phenomenon of uncertainty aversion, first exhibited in the context of Ellsberg’s thought experiments. In "Revising Non-Additive Priors", we consider the problem of updating such beliefs, in the presence of a signal of known (additive) likelihoods. Consider an employer who has a subjective prior over the quality of a worker and who knows the distribution for output conditioned on each level of quality. How does she update her beliefs regarding quality upon observing some output level? If her prior is additive, this problem is trivial: Bayes' rule suffices. This involves two steps: first, calculate the probability measure on the product space, of pairs of quality and output, and then use Bayes’ rule to calculate the posterior beliefs for quality.

When the employer's beliefs are represented by a capacity, calculating a measure over the product space is no longer so simple. We propose two rules: the first uses the idea of Choquet integration over identity functions and produces a non-additive measure over the product space; the second converts the initial non-additive measure to a set of additive priors, and then applies Bayes's rule to each element in this set. We show that these rules are related but are not equivalent. We argue that their non-equivalence highlights a limitation of non-additive measures. While this limitation does not matter for the representation of uncertainty-averse preferences, it results in a loss of information when beliefs have to be revised.