Lowest-unique sealed-bid auctions are auctions with endogenous participation, costly bids, and the lowest bid among all unique bids wins. Properties of symmetric NEs are studied. The symmetric NE with the lowest expected gains is the maximin outcome under symmetric strategies, and it is the solution to a mathematical program. Comparative statics for the number of bidders, the value of the item and the bidding cost are derived. The two bidders' auction is equivalent to the Hawk- Dove game. Simulations of replicator dynamics provide numerical evidence that the symmetric NE with the lowest expected gains is also asymptotically stable. © The Author(s) 2010.