The solution to the Tullock rent-seeking game when R > 2: mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government

Prizes and incentives

SIGLELD:D50094/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen in J Polit Econ 89:841–864, 1981). We find that it is often optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (1) R is small relative to P (where R is risk aversion and P is absolute prudence); (2) the distribution of shocks to output is asymmetric and the asymmetry takes a particular form; (3) the principal faces a limited liability constraint; and (4) there is agent heterogeneity of a particular form

Zur Reform der Professorenbesoldung in Deutschland*

The 'Gesetz zur Reform der Professorenbesoldung (ProfBesReformG)' lays down that the pay of German professors shall be linked more closely to their actual performance. Furthermore, total payment to all professors shall be fixed in advance. Combining both characteristics leads to an incentive scheme which is well known in labor economics - a tournament or contest, in which agents are rewarded according to relative performance. In this article, the results of the tournament theory are used to discuss possible advantages and disadvantages of the ProfBesReformG. In principle, the ministry of each federal state has to choose between two alternative ways in organizing a professors' tournament. There can be either a tournament within each faculty, or a tournament between different faculties. Unfortunately, both alternatives are problematic for different reasons. Copyright Verein für Socialpolitik und Blackwell Publishers Ltd, 2006