Sorry I didn't do economics... that may explain why I'm having trouble getting my head around this. I understand that taking either price as the price of the trade is OK with both parties - they're both willing to trade 10 and 10.5. The confusion is that as I understand it, markets use a price/time priority so as to reward earlier orders at the same price. So using that logic if markets are setup to reward earlier orders, why does the trade occur at a price that favours the newer order? Sorry if i'm being simple, I just can't see a good explanation.
The priority is in the timing benefits more so than the price, in that the seller that got in earlier at 10 will sell before the seller that also wants to sell at 10, but put his order in later. The buyer therefore buys from the first seller that put up the offer at 10, and thee second seller is stuck with his shares at 10. Timing doesn't overshadow price, however. If the current ask price is $10, the order won't fill at the much higher price of 10.5 because there will be other "suppliers" that are willing to sell at less than that anyway. While economics courses may not be necessary, I would suggest at least doing some extra reading on the most basic principle of supply and demand (look at the graphs especially - it will make sense to you) to clear this up a bit. See terms: demand, supply, equilibrium, surplus, shortage. Check out how various things affect the supply and demand curves and the equilibrium price. The rest builds on that.
factor in the reality that the high frequency traders that intentionally manipulate prices, destroy that simplistic, dated, original thinking method of trades matching and such, simply flood the electronic markets with bids all over the place so that on these penny variations, the ability to stop, pause, price match and then settle trades really never happens, under that pressure then the need to not hold an order at market and just basket execute all in a specified price range, say within plus / minus three cents, are all executed at the same price, and the process begins anew
Limit orders turns into a static order when they're not filled immediately. When you send an order with a limit price of 10.05, that effectively means, you want your order to be matched with every other order residing on the order book at that time, up to 10.05. Note that match happens on their price levels (because they're now static orders). The remaining unfilled part of your order will later reside on the order book at the limit price of your order till a new order hits your order. And this is the time when your order becomes static at your limit price level. This has nth. to do with time priority. Otherwise it would be almost impossible to implement a reliable order matching algorithm on performance basis.