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.