Essays on Dynamic Tournaments
This dissertation studies dynamic tournaments and their economic and managerial implications from two different perspectives. The first half focuses on the optimal timing of information release when a tournament uses a feedback scheme, while the other half investigates the impact of the use of mercy rule in a dynamic tournament on the economic output and other system wide characteristics.
In Chapter 2, we study dynamic tournaments in which time is modeled explicitly, as opposed to with the abstract notion of ``periods.'' By doing so, we characterize the effects of the ex-ante-designated timing of an interim progress report. Whether or not a policy of reporting increases total expected effort does not depend on the release time of the report, however the magnitude of the effect does. We demonstrate that total expected effort is single-peaked or single-troughed in the report's release time depending on parameters, with the peak/tough located at a time strictly more than halfway through the tournament. However, a policy of releasing information always harms the expected utility of the tournament's participants. Implications for tournament design are discussed.
Chaper 3 explores dynamic tournaments in a continuous space and continuous
time framework, in which contestants can observe their opponents' progresses
in real time and have the opportunity to end the contest early when one's
lead over the other is larger than some pre-determined threshold (a.k.a a
mercy rule). We first show that the game has a unique equilibrium, then characterize
the equilibrium numerically, and investigate the impacts of mercy rules on
tournament design. By doing so, we find that there exists an optimal mercy
rule that induces the best economic output, even though players always prefer a
tournament without a mercy rule. Depending on the cost and noises
parameters, a non-monotonic mercy rule may perform better. We also consider
the scenario in which players prefer to end the game early because of
outside options and have the choice to drop out. Given an exogenous mercy
rule, this drop-out option endogenizes another boundary. And surprisingly,
the endogenous mercy rule is not always dominated by the exogenous rule in
terms of inducing efforts.
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