We investigate the market effects of search advertising, within a model in which: there exist both sophisticated consumers (who look for any available information on their screen) and naïve consumers (who only look at the top link of their screen); and in which each firm chooses the price of its (differentiated) product and the bids for the advertising auction which is triggered by own and rival’s brand name search. Relative to a benchmark where only organic search exists, we find that advertising has two main detrimental effects on welfare: (i) if the owner of the brand wins its own brand name auction, the sponsored link crowds out the rival’s organic link thus reducing competition; (ii) the payment of the rival’s bid (may) raise marginal cost — in turn raising market prices. In a symmetric setting, we are unable to find situations in which search advertising may increase welfare. Under extreme asymmetry (there is an incumbent and an unknown new entrant), we do find that the market effect of brand name bidding might be beneficial, if the search engine does not list the entrant’s link in organic search, and the share of the sophisticated consumers in the economy is large enough for an equilibrium in which the entrant wins the advertising auction on the search for the incumbent’s brand to exist. (Work with Antonio Penta)