Faster trading improves liquidity in periodic call auction markets, in contrast to continuous-time markets. We build a model where high-frequency traders (HFTs) engage in duels to trade on stale quotes. More frequent periodic auctions increase the likelihood that a single HFT arrives in any given auction and subsequently acts as a monopolist on information. Higher trading speed increases the expected number of arbitrageurs participating in auctions, promoting competition between snipers and improving liquidity. We find that faster trading and longer auction intervals are substitute instruments to reduce bid-ask spreads. Relative to continuous-time trading, periodic batch auctions reduce HFT informational rents.