The reason I said the spread reverses is because while reading tony oz's book stock market wizard (basically a diary of him trading) there was such a situation. But it happened because in the US they have different exchanges (ARCA, NYSE, ISLD etc...) and, while you can see the best prices on all exchanges simultaneously, you can have a situation where the bid on ARCA is higher than the offer on ISLD. So yes, who ever was there first gets their price.