This paper examines the factors that lead liquidity-motivated investors to choose the type of market structure they prefer. We assume that investors can choose between a dealership and a limit-order-book market. This study builds a theoretical model for both the dealership and order-book markets and develops a numerical method to solve the Nash equiibrium strategies of heterogeneous market participants. We find that a dealership market would be preferred by investors in an environment where customer trading is relatively thin and correlated, and by investors who are subject to relatively large liquidity shocks.