The economic stakes of advertising on the Internet -and in particular, of auctions for keywords in search engines- are enormous and still increasing. We focus in this paper on situations where bidders (advertisers) on sponsored search auction systems have a limited budget, so that they may not be able to afford to participate in all auctions. Using a game-theoretical model of the strategic interactions among advertisers, we analyze the equilibrium strategies in terms of bidding frequencies, in the case of one monopoly search engine and when two search engines are in competition. Our results exhibit the importance for search engines to develop their attractiveness to customers, due to the impact this has on auction revenues.