The U.S. Supreme Court held that litigation for anticompetitive ends (“sham litigation”) must be “baseless” in order to face antitrust liability. The filing of such suits continues apace, as does the legal commentators’ debate, but economic analysis has lagged. Here, a game theoretic model is constructed in which plaintiffs file suit to achieve collateral gains and defendants may countersue for damages under the Sherman Act. In equilibrium, settlement fails and all suits are litigated, but the threat of countersuit deters low-expected-value plaintiffs. As the legal standard for sham litigation approaches “baselessness,” this deterrence effect is weakened and litigation may increase.