I used to work at a non-US exchange, and I can tell you that the exact answer to your question must be in that particular exchange’s rules, or in the SEC filings somewhere.
In my market, the “auction” was just a period where the answer to the question “at what price do we clear the most volume currently sitting in the order book?” was being calculated by the computer.
edit:
“Isn’t that just the price where the best bid matches the best ask?”
No, because matching stops for a little while before an auction. Also, you can place some orders that will only participate in the auction.
So your order book might have a whole lot of bids at different prices encroaching into the offer side (or vice versa). Unlike during continuous trading where I don’t think bids can cross into offers (because they’d be matched and removed).
The job of our auction computer was to figure out which of those price levels would remove the most volume from the book.
I think you'd line up all the buy orders by descending price, and line up all the sell orders by ascending price. Then there are three possibilities: the buy orders are exhausted, the sell orders are exhausted, or there are enough of each that their prices cross an equilibrium point.
In the latter case, you set the price at the crossing point, and clear all trades that you can at that price.
If the buys are exhausted, you set the price at the sell which clear it. And if the sells are exhausted, you set the price at the buy that will clear it.
It would, under such a system, be advantageous to always have some buys or sells put in that you don't expect to clear, but would produce profitable trades in case of sudden market moves in your favor.
In the past, that function would have been filled by the "market maker" trader.
The quote that follows is from a once-popular proposal for batch auctions that was essentially nixed by incumbents that profit from complexity in the existing market structure. You may want to check out pdf page 50 of [2] for a detailed description of the demand curves described in the quote.
"During the batch interval (e.g. 1 second), traders submit bids and asks as price-quantity pairs. At the conculsion of each batch interval, the exchange 'batches' all of the recieved orders and computes the market-level supply and demand curves. If supply and demand intersect, then all transactions occur at the same market-clearing price."
The demand curves can be degenerate, which means we have to address two edge cases: "Bids and asks of exactly the market-clearing price may get rationed (pro-rata). If there is a range of market-clearing prices, choose the midpoint"
