In this paper, we analyse how traders select marketplaces and bid in a setting with multiple competing marketplaces. Specifically, we use a fictitious play algorithm to analyse the traders' equilibrium strategies for market selection and bidding when their types are continuous. To achieve this, we first analyse traders' equilibrium bidding strategies in a single marketplace and find that they shade their offers in equilibrium and the degree to which they do this depends on the amount and types of fees that are charged by the marketplace. Building on this, we then analyse equilibrium strategies for traders in competing marketplaces in two particular cases. In the first, we assume that traders can only select one marketplace at a time. For this, we show that, in equilibrium, all traders who choose one of the marketplaces eventually converge to the same one. In the second case, we allow buyers to participate in multiple marketplaces at a time, while sellers can only select one marketplace. For this, we show that sellers eventually distribute in different marketplaces in equilibrium and that buyers shade less and sellers shade more in the equilibrium bidding strategy (since sellers have more market power than buyers).