Can a competitive market implement an ideal search engine? To address this question, we construct a two-sided market model in which consumers with limited, idiosyncratic vocabulary use keywords to search for their desired products. Firms get access to a keyword if they pay its competitive price-per-click. An underlying "broad match" function determines the probability with which a firm will enter the consumer's search pool as a function of the keyword it "buys" and the consumer's queried keyword. The main question we analyze is whether there exists a broad match function that gives rise to an efficient competitive equilibrium outcome. We provide necessary and sufficient conditions, in terms of the underlying search cost and the joint distribution over consumers' tastes and vocabulary, and characterize equilibrium keyword prices under such equilibria. The Bhattachayyara coefficient, a measure of closeness of probability distributions, turns out to play a key role in the analysis.
