It may be helpful to think of Alice trying to unload ten different stocks each at $10, every day M-F.

With HFT, some trades will go according to your first scenario; others will go according to the scenario you responded to. On net, Alice sells all her stocks to Eve and gathers in $100 every day.

If Eve stays home, instead Alice unloads perhaps six of her stocks to Bob at $10.05 each, and is still holding on to four of them. She doesn't want to end the day with $60.30 and four stocks she doesn't want, so she unloads the remaining stocks to Chuck and nets $100.10. Except that Chuck takes Mondays off, so on Monday she might end up selling to Chris and only finish with $99.90.

So what Eve (HFT) really accomplishes here is she grabs 10 cents of Alice's potential profit on most days or 10 cents of Alice's loss on Monday. Alice is happy with this arrangement because she gets the certainty of getting her $100 each day for the minimum effort. Eve is happy because she's grabbed an average profit of 6 cents per day (40 cents for T-F, -10 cents for M) in exchange for taking on a little bit of risk.

The real loser in this scenario is Freida, who is trying to do the same thing as Eve but is a little bit slower.

If Eve stays home, and Alice places a standing limit sell order at $10.00, and Bob comes along with a limit buy at $10.05, Alice's is the standing order and will set the price of the trade. The trade will fill at $10.00, not $10.05.

Alice isn't screwed in the second case. She just gets lucky in the first case.

Alice is holding a security that is decreasing in value, and her book order isn't going to clear.

Assuming no HFTs, maybe Alice could set min_price=9.9$, and still sell for $10.05 in the better scenario? It seems that HFT's kill alice's sell spread option, forcing her to sell at min_price?

Huh? If Alice places a limit sell at $9.90, Bob's limit buy at $10.05 order will execute at $9.90. The limit price of the standing order is the one that prices the trade.

Oh, thanks for correcting my misunderstanding. So in general, sell "min_price" really just means sell "price"? Or are there circumstances that it would sell above that price?

As explained above, if Bob's $10.05 buy order was in the order book first, then Alice's $9.90 sell order would trade with Bob's buy order at $10.05.