Four.

That's the magic number. There have to be four competitors of significant size before prices go down. There are both EU and US studies substantiating this. It's been seen in cellular phone networks, ISPs, drugstores, and banks. Drop below the threshold of four, and the magic happens. Prices go up, margins go up, and consumers lose.

Four should be the basis of antitrust policy. Less than four, and there are two options - break up, or become a regulated public utility.

Two or three isn't enough. Collusion happens. Explicitly or implicitly, price competition doesn't happen with only two or three players. Four seems to be enough that cartels usually break up on their own. Somebody won't play ball.

Four.