We revisit the two bidder complete information all-pay auction with bid-caps introduced by Che and Gale (1998), dropping their assumption that tie-breaking must be symmetric. Any choice of tie-breaking rule leads to a different set of Nash equilibria. Compared to the optimal bid-cap of Che and Gale, we obtain that in order to maximize the sum of bids, the designer prefers to set a less restrictive bid-cap combined with a tie-breaking rule which slightly favors the weaker bidder. Moreover, the designer is better off breaking ties deterministically in favor of the weak bidder than symmetrically.
Tie-Breaks and Bid-Caps in All-Pay Auctions
Games and Economic Behavior, 2015, Vol. 92, 138-149; DOI:10.1016/j.geb.2015.05.008