No, there is no such mechanism. Bitcoin leaves each miner entirely free to decide how to include valid transactions in the blocks they mine however they choose.
With less than 51% of mining power conspiring, at worst they could make transactions take about twice as long. With more than 51% of mining power conspiring, bitcoin loses a lot of its desirable properties.
A lot of things prevent this in practice though. For one thing, if there was evidence that 51% of mining power was actually conspiring to censor or blackmail, the users could get together and change the proof of work algorithm, rendering everyone's mining hardware useless. This is kind of the nuclear option for the users because it will also cost honest miners a lot of money and without honest miners, bitcoin is not useful or secure. Miners know that users have this nuclear option, so they're very unlikely to conspire in such an obvious way.
All miners mine blocks. If one miner does not mine some transaction other will. How can you offer a fee to all of them? – croraf – 2017-11-03T16:28:46.363
Well, as I said, it is more a thought experiment: Assume I can generate of some kind of trust regarding my actions. If I want to prevent bitcoin outflow from a certain wallet I can monitor if a transaction initiated from that wallet is awaiting to become part of the new block. I could offer to pay a fee if specific transaction is NOT included in the next block. – muffin1974 – 2017-11-03T16:34:10.670
So, you're trying to delay/censor a third party's payment? AFAIK, there's no built-in support in Bitcoin for that… – Murch – 2017-11-03T16:35:48.557
You should be a bit more specific of what would be the way of attack, as you cannot bribe a significant portion of miners. And each of them has the interest in mining that block to get a fee, so you would have to bribe majority of them. – croraf – 2017-11-03T16:39:25.297