I understand how limit orders work but I don't know how do they meet. Suppose the book of a ticker ABC is empty. Trader 1 sends a buy limit order for 1 share of ABC at 2\$, and at the same time (ideally speaking, simultaneously) Trader 2 sends a sell limit order for 1 share of ABC at 1$. What will be the transaction price?
In this question, the "accepted" answer says that it depends on the arrival position, it is a "race condition", so the last order to arrive will execute against the first.
If we suppose that Trader 1 was the first one to send the order by a microsecond, what does it mean this solution? What does it mean that Trader 2 will be executed against the price of Trader 1?
Does it mean that Trader 2 will sell at 2\$? So, here Trader 1 won't take full advantage trying to buy for less than 2$?