I think the price that one gets is up to the MMs. The brokers don't have much say. I had a bid in last week for a few days and each day shares were sold under my bid. I called eTrade and they said it's up to the MM and all they can do is to try to route it through another MM. It was a small order so I just increased my bid price.
In the past I found that bidding high gets shares quickly, and I still was able to get a good price. The orders below were all placed at $1 and filled at a much lower price, the same price others were getting. A grid from eTrade.
Right now bid sitting might be a better strategy, at that time high bids worked for me.
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