Asymmetric Contests with Head Starts and Nonmonotonic Costs

Abstract

This paper studies multiprize contests in which players' costs need not be strictly increasing in their performance. Such costs accommodate various types of asymmetries, including head starts. Head starts capture incumbency advantages, prior investments, and technological differences. I provide an algorithm that constructs the unique equilibrium in which players do not choose weakly- dominated strategies, and apply it to study multiprize all-pay auctions with head starts. A comparison to the standard all-pay auction shows that the strategic effects of head starts differ substantially from those of differing valuations. (JEL D11, D44)

Sourcing Innovation: Public and Private Feedback in Contests

“…The literature on complete information contests assumes that all characteristics of the players are observable. Early work has seeked to characterize equilibria in symmetric contests (e.g., Glazer and Hassin 1988), but that aim has been expanded to settings that feature asymmetric cost functions or valuations (e.g., Che and Gale 2003, Siegel 2009, 2014b. The literature on incomplete information contests assumes that each solver holds some piece of private information which is often framed as some type of individual capability.…”

Advances in Auctions

“…This analysis is extended to three or more heterogeneous players in Siegel (2009Siegel ( , 2010Siegel ( , 2014b. In addition to the analysis being an important and difficult technical achievement, Siegel finds that the equilibrium with three or more heterogeneous players can have qualitatively different behavior than in the two-heterogeneous-players model.…”

Revenue Maximizing Head Starts in Contests

“…However, this is challenging because there presumably exists a continuum of equilibria that are potentially not even revenue-equivalent (similar to the equilibrium characterization of the symmetric all-pay auction in Baye et al (1996), [2]). It should also be mentioned that our setup can neither be transformed into a symmetric all-pay auction, nor is it possible to apply Siegel (2014), [15], to (a transformed version of) our setup because his genericity assumption would preclude the use of the optimal head start δ * .…”

“…To our knowledge there only exist three studies that involve head starts in multi-player all-pay auction or lottery contest frameworks. While Siegel (2014), [15], considers head starts in multi-prize all-pay auctions, Wasser (2013), [17], incorporates homogeneous head starts in a lottery contest framework. However, both studies are rather interested in equilibrium characterization and not in the optimal design of the head starts.…”