I understand that retail brokers pass their customers' trades on to trading firms, and receive a payment for order flow in return. These trading firms carry out the trades and presumably also have to pay per-trade exchange fees to the stock exchanges. So if they pay to both sides, how can they make money?
A recent article in the New York Times (Robinhood Has Lured Young Traders, Sometimes With Devastating Results, 8 July 2020) described the setup thusly: "Each time a Robinhood customer trades, Wall Street firms actually buy or sell the shares and determine what price the customer gets. These firms pay Robinhood for the right to do this, because they then engage in a form of arbitrage by trying to buy or sell the stock for a profit over what they give the Robinhood customer." I have a hard time understanding this paragraph. Does it mean that the customer receives a worse price than is available at the stock exchange at the time, and the trading firm pockets the difference?