We study the determinants of asset market fragmentation in a model with strategic investors that disagree about the value of an asset. Investors’ choices determine the market structure. Fragmented markets are supported in equilibrium when disagreement between investors is low. In this case, investors take the same side of the market and are willing to trade in smaller markets with a higher price impact to face less competition when trading against a dealer. The maximum degree of market fragmentation increases as investors’ priors are more correlated. Dealers can benefit from fragmentation, but investors are always better off in centralized markets.