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I am learning a little bit about the bitcoin technology and I have some basic questions about its p2p and transaction processing.

First imagine that a bitcoin transaction has included a fee (maybe a high one). If a node, which can mine blocks receives it, why should it broadcast this information into the network? Wouldn't it be better for the miner just to add the transaction to the block and start mining as soon as possible without revealing this to the competition?

If this happens and the information is not propagated, it can happen that the miners who included this transaction are unlucky and can't find proof-of-work before others and the transaction gets stuck for a certain time. So my other question is: if only a part of the network knows about a transaction due to technical issues or malicious behavior, is it possible for the transaction to become stuck for quite a number of blocks before it enters into the blockchain?

Thank you!

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