This is actually a matter of exchange policy. Almost all exchanges go with the price on the older of the two orders in the match, but you need to check with the exchange to be sure if the exact behavior matters to you.
You should never tell an exchange that you are willing to accept a price that you aren't actually willing to accept.
No, almost all excahgnesa re obliged to give you the BEST price, MOST then match the oldest order at that price.
Talking SERIOUS exchagnes here - NYSE, NASDAQ, CBOT, CME, NYMEX, GLOBEX.
It is ALWAYS matching best price.