Yes. In my reply to the first comment I mentioned setting the opening price is "more complicated". Every exchange has their own system for the opening auction which you buy into when you list with a particular exchange. Most exchanges have an algorithmic way of calculating the price. For NYSE, it's again more historical. A Designated Market Maker (DMM) for a stock technically determines the opening price. There is a person physically on the NYSE trading floor who represents the DMM firm who technically opens the different stocks. They have a weird custom keyboard from NYSE for this purpose...

The price is usually calculated algorithmically by the DMM firm and sent to the person at NYSE to approve. Pretty arcane. Also somewhat shady, as the DMM firm can be and is part of the auction themselves. DMM firms can analyze the order book to see what the imbalance is in the overlapping region, and place an order of their own to correct the imbalance and then set the opening price. I can see how one can profit from this in certain situations