When games involve players being able to attack each other or ally with each other in a relatively unrestricted way, I generally feel that such games work best with only two sides. When there are more sides, certain characteristic things happen in the game that tend to overshadow the ordinary play of the game. I am referring to these developments of the game play as three-player game mechanics, as they tend to exemplify why it can be difficult to create a three-player game without careful thought to the game mechanic. The same things can happen with more players as well.
Perhaps the most classic 3-player game mechanic is the Alliance mechanic, where two players will form a semi-permanent alliance in order to knock the third player out of the game, before turning on each other. It is easier to win a 2-player game than a 3-player game, so it is very logical for 2 players to team up like this. And in the kind of games I'm discussing here, the third player is likely to have little or no chance of surviving against this kind of odds. So the most important part of game play is to be one of the players in the alliance. This is what I really think of with a game like Diplomacy. In my experience, given an average group of players, socializing among the players basically determines success, overwhelming any tactical or strategic considerations. Often the most persuasive player will convince the weakest player to join an alliance, hoping he can destroy the dangerous third player then eliminate his ally. The rules of the game don't make a whole lot of difference – the game is won or lost at the very beginning, when the alliances are formed.
In theory, when the alliance has just about crushed the third player, one of the alliance might want to suddenly backstab the other, thus allowing the third player to stay in the game. But this doesn't seem very likely unless the game is carefully constructed for it; there are many things that can prevent it. Sometimes attacking a weak player is very profitable in terms of stealing resources, so there is really no reason to attack your strong ally until the weak player is totally destroyed. Sometimes there isn't much of a gray area, by the time the alliance has done enough damage to consider turning on each other, the third player is hopelessly crippled. Sometimes the alliance has so many forces in the third player's territory that he'll be destroyed by the fighting anyways. Sometimes the game doesn't really allow the alliance players to catch each other with surprise attacks, so there is little incentive not to continue the alliance properly. Very often the personalities or social relationship of the players is such that they aren't inclined to terminate the alliance until its successful conclusion, regardless of other logic.
Another classic 3-player mechanic is the Balance of Power mechanic, in which player with the strongest position at any given time is opposed by the other two players, until that player is no longer the strongest. This mechanic is actually fairly popular, as it helps ensure that all players remain in the game. When this is done is a very weak way, it can be a nice mechanic for that purpose. But in the unrestrained format, it results in a game where any form of successful game play that is visible to the other players is meaningless, because they just team up to remove any advantage gained. So most of the game is just a formality, with no effect on the eventual outcome, unless a player can get some sort of secret advantage the others aren't aware of. Then, at the end of the game, it becomes a question of who chooses the right time to sprint for the finish line. Somewhat like the end of a cycling road race stage, where if you start your sprint too early, or too late, you lose. Very often the first player to come close to winning is just barely stopped, then another player sneaks in to victory.
A third mechanic is the Let's You and Him Fight mechanic. This is characteristic of games in which combat simply causes attrition to the attacker and the defender. In this sort of game, it is highly advantageous not to attack at all. If the two other players fight each other, you are the one that benefits. If all of the players realize this, then either the Alliance or Balance of Power mechanic takes over, or the game just goes on without combat, and is rather boring. Very often, however, if the game is about combat, the players will fight anyway, simply because there is no point playing if nothing is going to happen. And if they do, eventually a winner will be declared. But this means the game is creating a degenerate situation where trying to make the game fun causes you to lose the game – not a situation you want in your game.
If you are interested in a game of deception and tricky diplomatic maneuvering, the Alliance and Balance of Power mechanics can be very interesting. There are definitely games built around this sort of thing, such as Diplomacy. But if you don't want this to be the focus of the game, these 3-player mechanics are destructive, as they dominate the game play and make most of the actual game mechanics insignificant. The Let's You and Him Fight mechanic, as far as I can tell, is purely something destructive to be avoided.
If you don't want your multiplayer game to be dominated by one of these mechanics, they can be prevented or minimized by an appropriate game design; most popular multiplayer games do this. In many games players have strong reasons to be interested in improving their own unique position, and a very limited ability to concentrate attacks on specific players. But if you just take a good competitive two-player game, and add multiple sides, it is all too easy for the game to degenerate into one of these three-player mechanics and become a very different game.