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Essays on Contests, Identification and Agglomeration

  • Author(s): Kubitz, Gregory
  • Advisor(s): Copic, Jernej
  • et al.
Abstract

This manuscript consists of three essays divided into three chapters. The second chapter is an essay co-authored with Tiago Caruso, and the third chapter is a version of a collaborative project with Jernej Copic, Robert Sherman, and Omer Tamuz.

The first chapter studies repeated contests with private information. In these contests, weak contestants prefer to appear strong while strong contestants prefer to appear weak. In contrast to a single contest, this leads to an equilibrium where effort is not strictly monotonic in ability and allows for a less able contestant to win against a contestant of higher ability. While the aggregate payoffs of contestants are higher per contest than in the single contest benchmark, aggregate output per contest is lower. Depending on the economic setting, the presence of private information can lead to productive or allocational inefficiencies.

In the second chapter we study a binary choice model where an agent makes a decision that is informed by his beliefs after observing a public signal. This model generalizes to a wide range of economic environments which require econometricians to estimate the beliefs of agents. With minimal structure imposed on the agent's utility function, we characterize the structure of information needed to identify the beliefs of the agent after observing both signals and decisions. We find that the information must be sufficiently convincing and dense for the agent's beliefs to be point identified. When the full range of information is relaxed, we show how the agents beliefs can be partially identified. Additionally, we explicitly show how the econometrician can construct the sharpest boundaries around the agents beliefs, as she observes signals and decisions.

In the third chapter we propose a simple model of agglomeration of some particles (or agents) when there is no growth in the number of agents. In many periods, countably many agents move freely (randomly) along a line until they encounter other agents, in which case they form a community and stop moving. We show that as time goes to infinity, the distribution of sizes of communities is exponential. When agents can also detach (leave) a community, we show that when the probability of leaving a community decreases sufficiently fast with the community size, there is no steady-state distribution of community sizes: as time goes to infinity, community sizes tend to infinity.

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