When playing a game with three or more players, you have to consider more than just the mechanics of the game itself. You need to concern yourself with the diplomatic situation.
Whenever you make a decision in a multiplayer game, it is likely that you will be disadvantaging the other players, and some decisions can create greater or lesser disadvantages for different opponents.
Deciding who you disadvantage most or least will probably win you some friends or enemies in the game, which can alter those players’ decisions towards you later in the game. I’ve found that very few people can maintain a logical and detached style of play when a decision goes against them, in future they will act irrationally, looking to cause harm to the prospects of their new enemy, even to the point where it harms their own chances of winning.
So to succeed at multiplayer games, you have to master the diplomatic game as well as the mechanics of the game at hand. Offer alliances as required, make friends and reduce the number of enemies you create. You must try not to become a target of others enmity until you can be sure you hold a strong enough position to ignore it.
Learn the particular foibles of your regular play group, and work them to your advantage. Some players will hold a grudge, don’t give them a chance to get one in the first place. Some players will be loyal allies and some won’t. Learn who will be loyal, and seek alliances there rather than in less reliable quarters.
Regarding game design, you have a choice of how much player interaction you want to include in the game. The more interaction included, the more potential for diplomacy amongst your players. If players must compete for scarce resources, then this will increase the required diplomacy. If players must take actions together, then the opportunities for diplomacy will increase.
Any multiplayer game must have opportunities for diplomatic maneouvers, I think that you will generally seek a middle ground for providing these opportunities, too many and the game will take forever to play, as the players discuss their options all day. Too few, and the players may as well be playing solitare. Striking the balance somewhere in the middle is key, but finding the particular level you require will depend a lot on the game you are creating.
The diplomatic opportunities are important enough to consider as a key feature in your game design, almost with the initial idea, and certainly very early in your game process.