Asymmetric Contests with Conditional Investments

This paper studies equilibrium behavior in a class of games that models asymmetric competitions with unconditional and conditional investments. Such competitions include lobbying settings, labor-market tournaments, and R&D races, among others. I provide an algorithm that constructs the unique equilibrium in these games, and apply it to study competitions in which a fraction of each competitor’s investment is sunk and the rest is paid only by the winners. Complete-information all-pay auctions are a special case. (JEL D44,D72,J41,L13,C71) Rent-seeking scenarios, competitions for promotions, and research and development (R&D) races are examples of competitions in which participants expend resources regardless of whether they win or lose. Although similar in their “all-pay” feature, such competitions often differ in important dimensions. These include the type of technologies ∗Department of Economics, Northwestern University, Evanston, IL 60208 (e-mail: [email protected]). I am indebted to Ed Lazear and Ilya Segal for their continuous guidance and encouragement. I thank Jeremy Bulow for many beneficial discussions. I thank Yuval Salant for valuable feedback throughout my work on this project. I thank three referees for their valuable comments. I thank Wouter Dessein, Chaim Fershtman, Julio González-Díaz, Matthew Jackson, Sunil Kumar, Jonathan Levin, George Mailath, Stephen Morris, Marco Ottaviani, Philip Reny, Kareen Rozen, Andrzej Skrzypacz, Bruno Strulovici, Balázs Szentes, Michael Whinston, Robert Wilson, Eyal Winter, and seminar participants at Chicago, Chicago GSB, Columbia, Cornell, CSIO-IDEI, Hebrew University, Northwestern, NYU Stern, Penn State, Stanford, Tel-Aviv, Toronto, UPenn, Washington (St. Louis), Yale, and Yonsei for helpful comments and suggestions.