There has been some discussion about possible attacks if one has the majority (over 50%) of the computing power of the bitcoin network. What happens if an attacker (or coordinated group of attackers) has more computing power than any other user (or coordinated group of users), but not necessarily the majority of all computing power?
As a toy example, consider we have 3 users: Alice, Bob, and Steve.
Alice and Bob are both honest users that are fine using the protocol as specified. However, they will not go above-and-beyond the protocol to help each other (in fact, they would be happy to make money off the disadvantage of the other, as long as they are still complying with the protocol).
Steve is an attacker and is willing to perform actions outside of the protocol in order to either gain profit or just destroy the network. If Steve has 41% of the computing power, Bob has 34%, and Alice has 25% then are there attacks Steve could launch?
The toy example is included to just make it clear what I mean by plurality vs. majority, and what I mean by honest but uncoordinated users. I am obviously more interested in an answer to the general question than this specific toy model.