Order routing and market quality who benefits from internalization?

Does retail order internalization benefit (via price improvement) or harm (via reduced liquidity) retail traders? To answer this question, we compare two market designs that differ in their mode of liquidity provision: In the setting capturing retail order internalization, liquidity is provided by market makers (wholesalers) competing for the retail order flow in a Bertrand fashion. Instead, in the open exchange setting, price-taking competitive agents act as liquidity providers. We discover that, when liquidity providers are risk averse, routing of marketable orders to wholesalers is preferred by all retail traders: informed, uninformed, and noise. Furthermore, most measures of liquidity are unaffected by the market design. We also identify a universal parameter that allows comparison of market liquidity, profit and value of information across different markets.