Economics

We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. We also design a revenue-maximizing scheme for the case where customers are heterogeneous with respect to their waiting cost parameter. Now lower cost parameter customers are encouraged to join the premium class at a low price: Given that, those with high cost parameter would be willing to pay even more for this privilege.

We provide an exact analytical solution of the Nash equilibrium for the k th price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

Let V be a finite society whose members express weak orderings (hence also indifference, possibly) about two alternatives. We show a simple representation formula that is valid for all, and only, anonymous, non-manipulable, binary social choice functions on V . The number of such functions is 2 n+1 if V contains n agents.

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditional optimal mechanism design approach is ill-suited---either because it makes overly strong assumptions, or because it advocates overly complex designs. This survey reviews several common issues with optimal mechanisms, including exorbitant communication, computation, and informational requirements; and it presents several examples demonstrating that passing to the relaxed goal of an approximately optimal mechanism allows us to reason about fundamental questions that seem out of reach of the traditional theory.

We examine how the randomness of behavior and the flow of information between agents affect the formation of opinions. Our main research involves the process of opinion evolution, opinion clusters formation and studying the probability of sustaining opinion. The results show that opinion formation (clustering of opinion) is influenced by both flow of information between agents (interactions outside the closest neighbors) and randomness in adopting opinions.

We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our approach shows that dictatorships can be seen as fixpoints of a certain process.

Arrow's `impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the theory of voting, and the structure of tournaments. By identifying the objects of choice with mathematical sets, and preferences with Hausdorff measures of the distances between sets, it is possible to extend Arrow's arguments from a sociological to a mathematical setting. One consequence is that notions of reversibility can be expressed in terms of the relative configurations of patterns of sets.

We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated -- in terms of number of assignments -- in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium.

I study costly information acquisition in a two-sided matching problem, such as matching applicants to schools. An applicant's utility is a sum of common and idiosyncratic components. The idiosyncratic component is unknown to the applicant but can be learned at a cost. When applicants are assigned using an ordinal strategy-proof mechanism, too few acquire information, generating a significant welfare loss. Affirmative action and other realistic policies may lead to a Pareto improvement. As incentives to acquire information differ across mechanisms, ignoring such incentives may lead to incorrect welfare assessments, for example, in comparing a popular Immediate Assignment and an ordinal strategy-proof mechanism.

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. Current literature has characterized asymptotic behavior under fairly specific assumptions. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a generalization of a differential equation that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.