Assume that the quoted bid for a stock stays at $10.00 and the ask at $10.05. If I were to place a limit order to buy 1 share at $10.00, and someone else placed a limit order to sell 1 share at $10.00, would they ever sell their share to me, or would it always go to the specialist/market maker who bid $10.00?
This is what I believe: It depends on how the seller sells his shares (which brokerage firm). If his brokerage firm has preferred market makers, his order will be sent to those market makers. If the seller has direct access and uses ECNs... let's say he selects ARCA and you also participate in ARCA, then the ECN does a first-in-first-out matching for the same price.
The book bidding $10 would be satisfied in front of your $10 bid. Once the book gets cleaned out in front of you then you will be the high bid, assuming a $10.01 bid (or higher)does not come in. I am not an ECN maven so I can not comment on the other response, I use market(able) orders!
If you bid on a certain ECN like BATS and you're the only person there and the seller sells at 10 to BATS specifically then you will get filled first. If there are others already bidding on BATS then you will be the last to get filled on BATS. If someone sells a large order at 10 then it will depend on the routing strategy they use and the FIFO order. For example, something might first take everything on ARCA, then reroute to NYSE, then route out to the rest of the ECNs/liquidity pools. Also, my understanding is that odd lots placed on NYSE will jump the queue and get filled by the specialist first. I know this because I got a warning from the specialist for doing that with hundreds of 99 lot orders on the bid and ask one day, lol.