Equilibrium in dynamic economic models

The main theme running through these three chapters is that economic agents are often forced to respond to events that are not a direct result of their actions or other agents actions. The optimal response to these shocks will necessarily depend on agents' understanding of how these shocks arise. The economic environment in the first two chapters is analogous to the classic chain store game. In this setting, the addition of unintended trembles by the agents creates an environment better suited to reputation building. The third chapter considers the competitive equilibrium price dynamics in an overlapping generations environment when there are supply and demand shocks.

The first chapter is a game theoretic investigation of a reputation building game. A sequential equilibrium model, called the "error prone agents" model, is developed. In this model, agents believe that all actions are potentially subjected to an error process. Inclusion of this belief into the equilibrium calculation provides for a richer class of reputation building possibilities than when perfect implementation is assumed.

In the second chapter, maximum likelihood estimation is employed to test the consistency of this new model and other models with data from experiments run by other researchers that served as the basis for prominent papers in this field. The alternate models considered are essentially modifications to the standard sequential equilibrium. While some models perform quite well in that the nature of the modification seems to explain deviations from the sequential equilibrium quite well, the degree to which these modifications must be applied shows no consistency across different experimental designs.

The third chapter is a study of price dynamics in an overlapping generations model. It establishes the existence of a unique perfect-foresight competitive equilibrium price path in a pure exchange economy with a finite time horizon when there are arbitrarily many shocks to supply or demand. One main reason for the interest in this equilibrium is that overlapping generations environments are very fruitful for the study of price dynamics, especially in experimental settings. The perfect foresight assumption is an important place to start when examining these environments because it will produce the ex post socially efficient allocation of goods. This characteristic makes this a natural baseline to which other models of price dynamics could be compared.

An economic approach to consumer product ratings

In three essays we examine user-generated product ratings with aggregation. While recommendation systems have been studied extensively, this simple type of recommendation system has been neglected, despite its prevalence in the field. We develop a novel theoretical model of user-generated ratings. This model improves upon previous work in three ways: it considers rational agents and allows them to abstain from rating when rating is costly; it incorporates rating aggregation (such as averaging ratings); and it considers the effect on rating strategies of multiple simultaneous raters. In the first essay we provide a partial characterization of equilibrium behavior. In the second essay we test this theoretical model in laboratory, and in the third we apply established behavioral models to the data generated in the lab. This study provides clues to the prevalence of extreme-valued ratings in field implementations. We show theoretically that in equilibrium, ratings distributions do not represent the value distributions of sincere ratings. Indeed, we show that if rating strategies follow a set of regularity conditions, then in equilibrium the rate at which players participate is increasing in the extremity of agents' valuations of the product. This theoretical prediction is realized in the lab. We also find that human subjects show a disproportionate predilection for sincere rating, and that when they do send insincere ratings, they are almost always in the direction of exaggeration. Both sincere and exaggerated ratings occur with great frequency despite the fact that such rating strategies are not in subjects' best interest. We therefore apply the behavioral concepts of quantal response equilibrium (QRE) and cursed equilibrium (CE) to the experimental data. Together, these theories explain the data significantly better than does a theory of rational, Bayesian behavior -- accurately predicting key comparative statics. However, the theories fail to predict the high rates of sincerity, and it is clear that a better theory is needed.