Publication: Essay on contests and voting
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2016-06
Defense date
2017-01-10
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Abstract
This thesis has three chapters. In the first chapter I study the role of information in contests.
A contestant’s effort depends on her knowledge of her rival’s type. This knowledge is often
limited in real-life contests. I propose a model where the principal of a contest has
commitment power to verifiably disclose contestants’ types. I investigate the optimal
disclosure policy to stimulate contestants’ efforts. I find that full disclosure spurs more (less)
efforts than full concealment if the distribution of types is skewed toward high- (low-) types.
However, the optimal disclosure policy is a particular partial disclosure, regardless of the
skewness of the distribution of types; it consists of disclosing the signal which is best for the
principal (i.e., all contestants are high-types) and concealing the rest.
In the second chapter I propose a novel objective function of a contest designer. When the
winner selection process in a contest is noisy, the designer should take this noise into
consideration when designing the contest if her goal is to maximize the quality of the
winning entry. I propose an objective function that accommodates this idea, and I compare
the optimal contest design under this objective function to the one under the commonly
assumed maximization of sum of contestants’ efforts. I find that, contrarily to what
happened when the designer maximized the sum of efforts, the optimal contest design
changes in that a designer may now benefit from: unlevelled playing field, exclusion of weak
contestants, and weakening of the underdog.
In the third chapter, which is a joint work with Christos Mavridis, we contribute to the
literature on pivotal voter models. For small electorates, the probability of casting the
pivotal vote drives one’s willingness to vote, however the existence of costs of voting
incentivizes one’s abstention. In two-alternative pivotal-voter models, this trade-off has been
extensively studied under private information on the cost of voting. We complement the
literature by providing an analysis under complete information, extending the analysis of
Palfrey and Rosenthal [1983. A strategic calculus of voting. Public Choice. 41, 7-53]. If the
cost of voting is sufficiently high at least for supporters of one of the two alternatives, the
equilibrium is unique, and fully characterized. If instead the cost of voting is sufficiently low
for everyone, we characterize three classes of equilibria and we find that all equilibria must
belong to one of these three classes, regardless of the number of individuals. Furthermore we
focus on equilibria which are continuous in the cost of voting. We show that this equilibrium
refinement pins down a unique equilibrium. We conclude by discussing an application of our
findings to redistribution of wealth.
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Keywords
Economía matemática, Modelo matemático, Teoría de juegos