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


Calculate the nonce for the next block and send it occasionally.
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.
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.
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.