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Nasdaq trading under the scenes: market makers, ECNs, brokers. Who buys from and sells to whom?

In short: Equity markets are fragmented: it means to buy or sell shares, you connect (via a broker) to a server on which you send a message with a side (buy or sell), a max/min price and a quantity. … Note it means the broker does not choose that much with whom you trade. He can have agreements with other brokers to match your message inside the NBBO, but cannot worsen your price. …
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