Nash equilibria in all-pay auctions with discrete strategy space - Zheng Li (Kiel Institute for the World Economy (IfW), 2017)
Using two-player all-pay auctions, the author fully characterizes the Nash equilibrium under a discrete bidding strategy space. In particular, he shows that under the random tiebreaking rule, the cardinality of the set of Nash equilibrium depends on the parity of the reward size and a continuum of Nash equilibria exists. Additionally, when a simple favorone-sided tie-breaking rule is used, the equilibrium solution becomes independent of the reward size.
Keywords: D44; D72; 330; asymmetric Nash equilibrium; all-pay auction