Keep on fighting: The dynamics of head starts in all-pay auctions

We investigate a model of a series of contests in which a contestant's past and present success gives a head start over a rival in the future. How this advantage from winning affects contestants' efforts, whether the laggard gives up or keeps on fighting, and how the head start develops over time, are key issues. We find that the expected effort of the laggard will always be higher than the rival at some stage in the series of contests, and this is most likely to happen when at a large disadvantage or at a late stage in the series.