isn't miner collusion rational?

Question

suppose for the sake of argument that each individual miner has the same amount of hashing power of one hash per unit of time (a "tick").

the probability that a miner solves their block in the next tick increases with the number of hashes already checked, since the nonce space is finite.

colluding miners could agree to pay the coinbase transaction to the same address and thus work on solving exactly the same block. they could divide the nonce space amongst them and thus exhaust the nonce space faster than solo miners.

by agreeing to redistribute the rewards of their mining amongst them, the colluding miners have an expected payout for the next tick that increases faster than that of solo miners, since they are exhausting their nonce space faster.

so isn't it rational for miners to collude? could this create a tendency to monopoly in mining?

Answer 1

No. Your premise is wrong. There is no guarantee a solution exists in a range. If a miner exhausts a nonce range he changes other components of the block header. Mining is a Poisson process with each hash attempt independent of any others.

Hence, there is nothing to gain with this particular kind of collusion. Of course, pooled miners enjoy less variance than solo miners (which is legitimate), and there are other methods of attack.

Answer 2

the probability that a miner solves their block in the next tick increases with the number of hashes already checked, since the nonce space is finite.

This is false. The probability that a miner solves their block has nothing to do with the number of hashes already checked. A block is solved if the nonce produces a hash less than the difficulty. Neither of these things are affected by prior hashes checked.

The nonce space is finite. But the nonce space can contain zero block solutions, one block solution or even two block solutions.

A typical miner exhausts their nonce space and starts working on a different block several times each second. I have a miner behind me that mines at about 300GH/s. Since there are only 4 billion nonce values, it can try the full range of nonce values 75 times each second. Needless to say, most blocks are unmineable with any nonce, and you must try again with a different block.

The odds of a block being mineable with any nonce are less than 3 billion to one.

Answer 3

Most of your question described a mining pool, and the motivation to form one.

Indeed it is rational to collude, and we have seen that as one of the earliest developments in the Bitcoin network. Also see: What is a Mining Pool, what is it good for?

Now, why don't we see only one mining pool? It's simple: Because it would be bad for the network! If one party controls too much of the network, i.e. 51% of the hashing power, they can control which transactions make it into the blockchain and get 100% of the mining rewards. This would quickly erode the trust in the network, and devalue bitcoins. For more information please refer to What can an attacker with 51% of hash power do?

Therefore miners, as people who are heavily invested in Bitcoin, are interested in keeping the mining power distributed. For example the mining pool GHash.IO has sent miners away when they were above 35% of the networks hashing power.

Answer 4

The current hash rate of the entire network is in the order of 2^55 hashes/sec.; in 10 minutes (less than 2^9 seconds), we would be running through 2^64 hashes/second. This is 1/2^96th of the available space (between all of us), if EVERYONE colludes. The chance of randomly chosen nonces colliding is outweighed by the effort it would take.

Also remember that, in that 2^160 space, there are a LOT of answers.