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We study asset liquidity in a model where financial assets can be liquidated for money in over-the-counter (OTC) secondary markets, in response to random liquidity needs. Traders choose to enter the market where they expect to find the best terms, understanding that their chances to trade depend on the entry decision of other investors. We find that small differences in OTC microstructure can induce very large differences in the relative liquidity of two assets. We use our model to rationalize, qualitatively and quantitatively, the superior liquidity of U.S. Treasuries over equally safe corporate debt. (Copyright: Elsevier)