How does quotation transparency affect financial market performance? Biais's irrelevance proposition in 1993 shows that centralized markets yield the same expected bid–ask spreads as fragmented markets, other things equal. However, de Frutos and Manzano demonstrated in 2002 that expected spreads in fragmented markets are smaller and market participants prefer to trade in fragmented markets. This paper introduces liquidity traders' costs of searching for a better quote into the Biais model and derives opposite conclusions to these previous studies: expected spreads in centralized markets are smaller and liquidity traders prefer centralized markets, while market makers prefer fragmented markets.