user101543: What prevents that certain miners and the blocks they can contribute to the chain are not ignored? What do the other participants in the network gain from  accepting their answers to the puzzle?

user24925: Bitcoin miners are anonymous. There’s no identifying information in blocks that could be used to censor a particular participant. The attributions for miners shown on block explorers are guesswork presented as fact. 

user7272: 
What do the other participants in the network gain from accepting their answers to the puzzle?

Essentially, consensus.
As long as a miner controls less than 51% of the network hashrate, they must always try to mine on top of the newest block.
If miner A creates block 1000, miner B may ignore it. Let's say B controls 20% of the hashrate. If B continues to mine on block 999, there is an 80% chance that another miner will produce block 1001, linking back to block 1000 - now B needs to find a block for heights 1000 and 1001 to keep up, and is currently out of sync with the network. This gap only grows as more blocks are added to the longer chain (which again will happen more frequently than B discovering a block and working to catch up).
Now, B has found no blocks, and receives no reward - instead, if B accepts A's block 1000 and continues mining on top of the newest block consistently, there is a 20% chance that they will receive the block reward + fees as the block will be part of the main chain the moment is is produced, instead of only being accepted after B is able to produce enough blocks to bridge the gap, which will (probably) not happen until B's hashrate is >=51% of the network hashrate.

user85: Miners don't mine for fun or out of generosity. They mine because they want to get the block reward and the transaction fees. Clients are programmed to choose the "longest" chain, that is, the one that took the most mining work to produce.
Now, say you're a miner who has 1% of the network's hash rate. You're trying to mine block 50,000 when someone else mines a new block 50,000. You have two choices, you can try to mine another block 50,000 or you can try to mine block 50,001 on top of the new one.
If you successfully mine another block 50,000, there is a very low chance anyone will accept it. They already have a block 50,000. However, if you successfully mine a new block 50,001, everyone will accept it because it allows them the chance to mine a longer chain rather than an equally-long chain.
Essentially, because the longest chain wins, everyone wants to mine a block on the longest chain they can. That means that unless you control a huge percentage of the mining power and have a realistic chance of mining two or more blocks in a row, you always want to mine on top of any new block that lengthens the chain.
(By "longest", I mean the one that took the most work to produce.)

101543: <p>What prevents that certain miners and the blocks they can contribute to the chain are not ignored? What do the other participants in the network gain from  accepting their answers to the puzzle?</p>
 24925: <p>Bitcoin miners are anonymous. There’s no identifying information in blocks that could be used to censor a particular participant. The attributions for miners shown on block explorers are guesswork presented as fact. </p>
 7272: <blockquote>
  <p>What do the other participants in the network gain from accepting their answers to the puzzle?</p>
</blockquote>

<p>Essentially, consensus.</p>

<p>As long as a miner controls less than 51% of the network hashrate, they must always try to mine on top of the newest block.</p>

<p>If miner A creates block 1000, miner B may ignore it. Let's say B controls 20% of the hashrate. If B continues to mine on block 999, there is an 80% chance that another miner will produce block 1001, linking back to block 1000 - now B needs to find a block for heights 1000 <em>and</em> 1001 to keep up, and is currently out of sync with the network. This gap only grows as more blocks are added to the longer chain (which again will happen more frequently than B discovering a block and working to catch up).</p>

<p>Now, B has found no blocks, and receives no reward - instead, if B accepts A's block 1000 and continues mining on top of the newest block consistently, there is a 20% chance that they will receive the block reward + fees as the block will be part of the main chain the moment is is produced, instead of only being accepted after B is able to produce enough blocks to bridge the gap, which will (probably) not happen until B's hashrate is >=51% of the network hashrate.</p>
 85: <p>Miners don't mine for fun or out of generosity. They mine because they want to get the block reward and the transaction fees. Clients are programmed to choose the "longest" chain, that is, the one that took the most mining work to produce.</p>

<p>Now, say you're a miner who has 1% of the network's hash rate. You're trying to mine block 50,000 when someone else mines a new block 50,000. You have two choices, you can try to mine another block 50,000 or you can try to mine block 50,001 on top of the new one.</p>

<p>If you successfully mine another block 50,000, there is a very low chance anyone will accept it. They already have a block 50,000. However, if you successfully mine a new block 50,001, everyone will accept it because it allows them the chance to mine a <em>longer</em> chain rather than an equally-long chain.</p>

<p>Essentially, because the longest chain wins, everyone wants to mine a block on the longest chain they can. That means that unless you control a huge percentage of the mining power and have a realistic chance of mining two or more blocks in a row, you always want to mine on top of any new block that lengthens the chain.</p>

<p>(By "longest", I mean the one that took the most work to produce.)</p>
