In some industries, more competition can very well hinder innovation. The subject of monopoly and innovation isn't clear cut- However, competition does foster more productivity, this is because of how competition alongside shareholder control fosters a dynamic framework of accountability wherein economic agents are responsible to the outcomes of their decision: Stockholders want profit for their investment, and as long as the directors provide this there wont be any problems. Hence, lower-management is made accountable to both directors and consumers, and through them workers.
I'd argue that alternatives to competition can exist in some specific circumstances. For example, railway privatization combined with land value capture mechanisms create a profit-motive to reduce prices and improve efficiency in railway services, irrespective of rail-profits. The reason being the improved accessibility generated by both increase the value of affected land, and hence, helps raise the aggregate profit for the firm through land value ownership i.e. land value capture.
I'd recommend this article on the subject of monopoly and innovation, http://www.hopesandfears.com/hopes/now/question/216743-is-competition-or-monopoly-more-innovative
