Simple Equilibria in General Contests*
Spencer Bastani†
Thomas Giebe‡
Oliver Gürtler§
First version: December 3, 2019 This version: May 17, 2021
Abstract
We show how symmetric equilibria emerge in general two-player contests in which skill and effort are combined to produce output according to a general production technology and players have skills drawn from different distributions. We also show how contests with heterogeneous production technologies, cost functions and prizes can be analyzed in a surprisingly simple manner using a transformed contest that has a symmetric equilibrium. Our paper provides intuition regarding how the contest components interact to determine the incentive to exert effort, sheds new light on classic comparative statics results, and discusses the implications for the optimal composition of teams.
Keywords: contest theory, symmetric equilibrium, heterogeneity, risk, stochastic dominance
JEL classification: C72, D74, D81, J23, M51
*An earlier working paper version of this paper was circulated under the title "A General Framework for Studying Contests". We thank Peter Cramton, Qiang Fu, Stephan Lauermann, Mark Le Quement, Johannes Münster, Christoph Schottmüller, Dirk Sliwka, Lennart Struth, Zhenda Yin, seminar participants at the University of Cologne, the University of East Anglia, the Berlin-Munich Behavioral Seminar, conference participants at the EALE SOLE AASLE World Conference 2020, the CMID20 Conference on Mechanism and Institution Design in Klagenfurt, and the 2020 Annual Meeting of the Verein für Socialpolitik for helpful comments. All authors gratefully acknowledge financial support from the Jan Wallander and Tom Hedelius Foundation (grant no. P18-0208). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC 2126/1 390838866.
†Institute for Evaluation of Labour Market and Education Policy (IFAU) and Research Institute of Industrial Economics (IFN); Uppsala Center for Fiscal Studies; Uppsala Center for Labor Studies; CESifo. E-mail: spencer.bastani@ifau.uu.se.
‡Department of Economics and Statistics, School of Business and Economics, Linnaeus University, Sweden. E-mail: thomas.giebe@lnu.se.
§Department of Economics, University of Cologne, Germany. E-mail: oliver.guentler@uni-koeln.de