As I previously mentioned, please clarify the terms that you use. You use price as both last trade and order interchangeably, which is not correct and leads to confusion.

Define:
Last Trade: amount that the trade last executed.
Order: Bid or Ask order on the order books.

So, let's use your example of bid/ask $10.00/$10.05 and last trade of $10.03
You place a buy order at $10.20.

What you are suggesting is that the market sees if there is a sell order at $10.03. If there is, it executes. If there is not, it moves to $10.04. Again, it checks to see if there are any available sell orders at $10.04. If not, it goes to $10.05 and sees if there are any sell orders at $10.05. Since $10.05 is at the top of the order book, the trade executes.

Am I understanding this correctly? We both agree that in this given state, the trade will never execute at any other price other than $10.05.

So, you added that a seller comes along and places an ask order at $9.90. We now have a crossed book (bid greater than ask). So what price does this execute at? You suggest $10.03 because that was the last trade.

I would argue that this would be incorrect.

Let's take the scenario of a low volume security. Let's say it's a far out of the money or far in the money option. If you follow the market, you'll see that often times, the volume of these trades are maybe 1 or 2 trades per day. You will often see that the Last Executed price is often either above the bid/ask spread or below the bid/ask spread.

Take for example, CAT Jan 14 $110 PUT. Last trade is $20.45. Current Bid/Ask Spread is $21.80/$22.15. The last trade is almost 7% discount of current market value.

So, let's use this CAT example. Current order book shows $21.80/$22.15. Last trade is $20.45. A buyer comes in with an order at $25 and a seller comes in with an order at $20. What price gets executed?

>Even if there are buyers and sellers who are willing to trade at a different price right now, the exchange won't allow that trade to complete until the price set by the exchange goes into a range where that trade can happen.
Please explain this sentence further. It makes little sense.
The only way that buyers and sellers can trade is if they cross the bid-ask spread. If you are saying that two other people are willing to make a trade, that means that they've cross the bid-ask spread. In theory, the "price" that you mention should be in the middle of the bid-ask spread.

Let's use a concrete example:
Going back to your $10.00/10.05 - last trade: $10.03
Am I understanding correctly that if someone places a buy order at $10.05 (ie order book $10.05/$10.05; last trade: 10.03) that that trade will not get executed? What happens in that scenario? Does the price rise to $10.04? (ie order book: $10.05/$10.05; "price": $10.04) In this case, the trade does not execute neither, even though two people are willing to trade at $10.05. So the "price" rises to $10.05 and the trade executes.
If this is the case, as a trader, I would front run the seller at $10.05 and put a sell order at $10.04. Anyone that sets a long dated limit order will be at an disadvantage; this will encourage speed.

In this type of market mechanism, you'll see more trades move to OTC. If I find another individual that is willing to make a trade, I will do it off the exchange rather than on the exchange.

Lastly, please explain how you would be able to distinguish between an HFT trader and a regular trader? Does it make a difference? Why is it better for individual investors that they only trade with other investors?

>but they have an improved opportunity of making trades in the middle of the range that market makers would be willing to offer.
This currently happens as it is. By SEC regulation, brokers are required to find the National Best Bid/Offer (NBBO) when you make a trade. In addition to this, brokers can perform Price Improvement actions and execute trades at better than NBBO (ie buy lower than ask/sell greater than bid). For example, ETrade has an 85.5% rate of price improvement. (https://us.etrade.com/e/t/activetrading/apptemplate?gxml=sca...)

Incidentally, I wrote a post about this market mechanism here: http://www.fatwallet.com/forums/finance/1004723/

Please forgive me if I am not understanding what your are suggesting, but a lot of what you are suggesting seems like it will not work in the real world.