We analyze a search engine market from a law and economics perspective and incorporate the choice of quality-improving innovations by a search engine platform in a two-sided model of Internet search engine. In the proposed framework, we first discuss the legal issues the search engine market raises for antitrust policy through analysis of several types of abusive behavior by the dominant platform. We also explore possible consequences of monopolization of the search engine market for advertisers and users in the form of excessive pricing and deterioration of the quality of the search results. Second, in the technical analysis part, we incorporate these considerations in a two-sided market model and analyze the rate of innovation, pricing, and quality choices by the dominant search engine. Our findings show that a dominant monopoly platform results in higher prices and underinvestment in quality-improving innovations by a search engine relative to the social optimum. More generally, we show that monopoly is sub-optimal in terms of harm to advertisers in the form of excessive prices, harm to users in the form of reduction in quality of search results, as well as harm to the society in the form of lower innovation rates in the industry. © The Author (2012). Published by Oxford University Press. All rights reserved.