“Head Starts in All-Pay Contests” by Ron Siegel
This paper studies equilibrium behavior in a class of games that models asymmetric multiprize competitions in which players' costs are non-decreasing. Such costs accommodate head starts, which can be used to model incumbency advantages, prior investments, and other asymmetries not captured by differences in players' marginal costs. Building on the results of Siegel (2009a,b), I provide an algorithm that constructs the unique equilibrium in which players do not choose weakly-dominated strategies. I apply the algorithm to study multiprize all-pay auctions with head starts, and compare the results to the existing ones regarding all-pay auctions without head starts. I also demonstrate the usefulness of the framework for contest design.