I suspect that the question about the price discovery mechanism of gas/Ether was not studied very deeply by the Ethereum developers.
The mechanism that currently exists must work by miners adaptively changing the lower bound of Ether per gas (asking price), and creators of transactions - offering certain prices and watching if the transactions get mined.
Number 0.05e12 wei, or its order of magnitude, most probably came out these sort of calculations: we have 5 ether per block mining reward, or 5e18 wei. One transaction costs at least 21000 gas. If every miner, after receiving the reward, spent all the ether on sending transaction, how many should they be able to send per second? If we allow around 3000 per second, then we can arrive at the right order magnitude for the current gas price.
Let me now make a little diversion.
Since miners do not current have a way to advertise what their current asking prices are, the transaction creators are effectively making 'blind' bids in hope that they will be equal or higher than the asking price (but not much higher). Also, the miner do not have a way of explicitly rejecting the bids when they are too low. So the bidders have to assume rejections implicitly, seeing that their transaction did not make it into the next block. That, of course, does not mean that all miners would reject the bid, only the one that happened to mine that block.
From above it should be obvious, that the current state of the gas price discovery is very inconvenient and inefficient. Therefore, some explicit market mechanisms would need to be added either to the protocol, or in a form of contract. This is probably easier to do post Proof-Of-Stake, because offer prices can be signed and relayed as ordinary transactions. But even now it would be possible to create such a contract, 'gas market' :)
Gas is burned for units of work, like gas in your car is burned by miles. Different fees for different operations. A transaction will burn a certain amount of gas.
GasPrice is like the price at the pump. What you are willing to pay for work. Miners will prioritize transactions with a higher bid for gasPrice.
If a transaction runs out of gas before finishing, the transaction fails and the gas is consumed from the effort.
If a transaction is disallowed, you pay for the gas to make that determination. This is because there is usually no way to know if the transaction will succeed or fail without running it.
Reducing the gas you send with the transaction probably leads to failure. Playing with the gasPrice adjusts the cost and the confirmation time.
Hope it helps.
Best Answer
You'll have to send a new transaction with the same nonce and the new gasPrice. Remember, you'll usually be only able to increase gas price, not decrease it.