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I purchased some Bitcoin through a local bitcoin ATM. When I purchased the Bitcoins I was not given an option to ad a transaction fee and currently it sits unconfirmed.
I also have a app on my iPhone that I have just started using to manage my Bitcoin called Bitwallet and in its 'Pay' screen it also does not offer an option to include a fee.
What are you meant to do to confirm transactions if no option for a transaction fee is ever offered?
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As Nick says, there really isn't anything you can do by yourself. The transaction fee has to be included when the sender creates the transaction.
There is a provision for transactions to be confirmed without fee, based on a "priority" measure that depends on the size of the transaction, and the length of time since those coins were previously spent. As such, the priority increases over time, so the transaction should eventually be confirmed, though the length of time depends on the size of the transaction. (The size may be larger than the amount due to you, if it includes payments to other people or an amount being returned as "change".) If you have the transaction ID, you can look it up on a block explorer like blockchain.info and see the priority.
If it doesn't confirm in a reasonable length of time, all you can do is take it up with the ATM operator. In principle, they can try to retract an unconfirmed transaction (by double spending) and issue a replacement or a refund.
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You don't do anything. The blockchain confirms for you that the ATM sent you some money. And as the receiver, you do not pay any transaction fee per se. Only the sender does.
1But the transaction is showing us unconfirmed and fees: 0 – McShaman – 2015-01-13T21:10:45.730
1 Are you looking on the receipt? On the blockchain? Put your address into here and see if you can find it: https://blockchain.info/
Although it won't help with your present situation, perhaps contact the ATM vendor and suggest that they consider doing what they can to improve this experience -- it's probably in their best self-interest. – Chuck Batson – 2015-01-14T17:24:06.347