Where does the money go if ask is lower than bid?

Question

If a stock has a current ask of €30,-, and I place a bid of €31,-, I assume my order would get matched with the ask order of €30,-. Where does the €1,- difference go? Do I buy the stock for €30,50, does the asker get lucky, the bidder get lucky, or does the €1,- "disappear" into the system (e.g. the broker)?
To answer some questions:

For the sake of the question I assume there are no fees involved.
Why would I offer more? I could see this happen in two scenarios:

A very volatile market, in which the price is going up rapidly, if I want to make sure I get the stock.
I place my bid slightly higher than the last bid, and at the same time someone places an ask to match the previous bid. (In this case it'll be a matter of cents instead of €1,-, but I'm assuming the mechanics are the same.)

Bob Baerker · Accepted Answer

Here's what happens in the U.S.  I assume that it's the same where you are and I'll describe it as such.
If you place a limit  order to buy fewer shares than the size available at the ask price of €30 then you'll buy shares at €30.
If you place a limit  order to buy more shares  than the size available at the ask price of €30 then you'll buy some shares at €30 and some additional shares above €30 (if they're available) up to a price of €31.  If there are enough additional shares available below €31 then your entire order will be filled.
If you have All Or None orders as we do, then you'll only get a complete fill if there were enough shares available below  €31 to fill your order otherwise you'll get nothing.

Rocky · Answer

The difference between the buy and ask is called the "spread".
Most bids and asks are matched by computer these days, with the the market makers taking the profit from the spread. Market makers are large trading firms, brokerages, and other entities standing by to always buy or sell certain high-liquidity stocks, thus facilitating the ask and bid (with a spread for profit), almost like a form of arbitrage since the spreads are usually slim when volume is large.
For low-liquidity stocks, there will usually be a larger spread, with the broker profiting from the difference.
The spread is created by the buyers and sellers themselves just by having open orders at the price they want to trade. In other words, the spread happens naturally from open orders waiting to be filled.

RockPaperLz- Mask it or Casket · Answer

If shares are available at €30, and you offer to pay €31, a good brokerage will settle the sale at €30.  They automatically recognize that there is no need for you to overpay €1 when the equity was available for €30.
Thus, you pay €30 and the seller gets €30.
Some brokerages are reportedly better than others at getting the best available price.
Also, some brokerages still charge to buy/sell equities, but these days, most do not.
There's also a small transaction fee, but it's so small they are counting on you not noticing it, or likely not even being aware of it.  There is big money in those transaction fees when you add them up for hundreds of millions of transactions.

Where does the money go if ask is lower than bid?

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