Auto pricing stocks in the pits

The key thing to remember is the pit is just price matching such that the pit boss does not end not with a pile of the stock.

The pit boss is faced with a series of bids coming in as an upper and lower valuer, both buy and sell.  First, treat every trade as a singleton, and the pit boss collects the largest window it can t=i which buyer and seller have some minimal overlap.  Two conditions, sufficient overlap and sufficient widow size, otherwise the pit boss cannot fairly price. The pit boss os constrained to owning a very small share of the market, but it has to pick up marginal price glows to make the buy and sell generators isonornormal. And, to pile on, let us not forget all trader have balance sheet uncertainty on the published data for the stock.

All parties now the constraint, the pit boss will adjust the price such that its holdings, in quantity, does not exceed its contracted price risk.  Everything is simpler when quantity per trade is fixed for everyone, and their bots are smart enough to parcel out the total, user requested trade.

There is more than one way to skin this cat, all of the various methods of stock trading, most can find their sandbox niche, including transaction timeouts. Multiple solutions, remember, are a characteristic because the pit boss actions are observable, within any pit and across pits.

So, pricing a stock, in different quantities per pit simply creates a cross tradebook uncertainty that is less than any individual tradebook uncertainty of all pits. All the trading bots observe an uncertain price/volume ratio. But  some trading bot in some volume quantized pit faces a greater, local uncertainty.