  When opposing parties compete for a prize, the sunk effort players exert
during the conflict can affect the value of the winner's reward. These
spillovers can have substantial influence on the equilibrium behavior of
participants in applications such as lobbying, warfare, labor tournaments,
marketing, and R&D races. To understand this influence, we study a general
class of asymmetric, two-player all-pay auctions where we allow for spillovers
in each player's reward. The link between participants' efforts and rewards
yields novel effects -- in particular, players with higher costs and lower
values than their opponent sometimes extract larger payoffs.
