A main idea is to use different strategies depending on the player.
Consider the case N=1: there are two players.
Suppose player 1 says the colour he sees, while player 2 says the opposite of the colour he sees.
Then: if both players have same colour, then player 1 wins, and if they have different colour, then player 2 wins. (I love it!)
Thus at least one player wins in any case.
In order to generalize to 2N players, simply group them by pairs and procede like above inside each pair. This way, exactly N players win every time. (But of course we don't know which ones)
That's as simple as that!