Abstract
We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.
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I thank co-editor Dan Kovenock and anonymous referees for detailed suggestions that substantially improved the paper. For valuable comments, I am grateful to Philipp Denter, Jörg Franke, Thomas Giebe, Ulrich Kamecke, Yvan Lengwiler, Johannes Münster, Georg Nöldeke, Roland Strausz, Elmar Wolfstetter, participants at the 2009 Workshop on Contests and Tournaments in Magdeburg, the 4th End-Of-Year Conference of Swiss Economists Abroad, the 2010 Meeting of the Swiss Society of Economics and Statistics, the 25th Congress of the EEA, and the 2010 conference of the Verein für Socialpolitik, as well as seminar participants in Cologne. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged.
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Wasser, C. Incomplete information in rent-seeking contests. Econ Theory 53, 239–268 (2013). https://doi.org/10.1007/s00199-011-0688-5
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DOI: https://doi.org/10.1007/s00199-011-0688-5