The bookkeeper of BitCoin is called a ‘miner’ today; Early in Bitcoin’s life his incentive is the new coins that arise as a byproduct of the agreed upon protocols. The miner gets to keep these coins. These protocols decree an end to this new money sometime after a predetermined number of bitcoins have come into existence. At that time incentives to keep the books will shift over to a scheme already in place—the transaction fee which the transaction originator determines as he creates the transaction. The fee is collected by which ever bookkeeper gets his books accepted which he does by working fast. Today that fee is a small part of the incentive. (8 or 17 US cents from a very small sample early in 2017. There are rumors of $5 fees in July.) Today there are consensus limits on block size and a miner will exclude transactions with lower fees to conform to the size limit.
It was not initially obvious to me how a stable transaction fees arise by price discovery. Here is what I have decided is probably the natural and only mechanism.
A miner gets signed transactions directly or indirectly from would be payers. A transaction refers to: