Inventors and producers bargain over royalties to license multiple patented inventions. In the first stage of the bargaining game, inventors offer licenses to producers and producers demand licenses. In the second stage of the game, inventors and producers engage in bilateral bargaining over licensing royalties. The analysis shows that there is a unique weakly dominant strategy equilibrium in license offers. The main result is that this bargaining procedure maximizes the joint profits of inventors and producers. Licensing royalties are less than bundled monopoly royalties. The efficiency of the bargaining outcome contrasts with the inefficiency of patent royalties in the Cournot model. The analysis explores the implications of the main results for antitrust policy concerns including Standard Essential Patent holdup, royalty stacking, patent thickets, the tragedy of the anticommons, and justification for patent pools. The discussion also considers how imperfect intellectual property rights affect bargaining over royalties.