Are competing blocks a problem to weak participant of the network?

Question

Let's say Alice has two CPUs, and Bob has only one. Let's assume Alice and Bob are the only miners in the Bitcoin network.

What will happen if Alice did the following:

1. Calculate the nonce for the next block and send it occasionally.
2. Whenever Bob solves and transmits a block, DON'T accept his block, but instead try to solve another block at the same height, and a successive block.
3. When done calculating, send both blocks to the network. They should be accepted instead of Bob's transaction, and since you're 2 times speedier than Bob, in average you'll be able to prevent Bob from mining coins.

While this is a somewhat artificial example, I think that it might represent a real problem. A group of strong participants can prevent weaker players from mining, even if this group does not control the majority of CPU resources in the network.

Answer 1

This isn't something that can happen unintentionally. If everyone plays by the rules, someone who has x% of the hashrate will find x% of the blocks, no matter how small or large x is (of course, for very small x the variance will be substantial, but without any change in the expectation).

You can attempt a double spend even without having >50% hashrate, but the probability of success is small. The chance improves as your hashrate approaches 50%. What's special about >50% is that you are guaranteed eventual success, no matter how many blocks the receiver waits.

There's a little-known attack (discussed here and here) that allows you to find more blocks than your hashrate normally allows, which doesn't require >50%. It still requires a relatively large hashrate, about 41%. For example, with 46% of the hashrate you can get 51.29% of the total blocks. For >50% hashrate you get 100% of the blocks.

Answer 2

That is essentially a 51% attack. It is a very real, but unlikely threat to the Bitcoin network. Historically as it turns out, it is more lucrative to simply add more processing power to the network than fight it.