So I’m reading this cool book on board game design. The book is a collection of essays, some better than others. In the first, Lewis Pulsipher poses some solutions to the three player problem and petty diplomacy. He goes into some detail to define the problems (check the link) and present the answers he has tested inside the rules circle of games.
I suggest an addendum. First, add social pressure. Unfortunately, not all players will be susceptible to that.
Second, and more helpfully, systemize social pressure in the form of cross-game scoring with the introduction an organized metagame. For example, play a card game in which you track points (whether for money or just bragging rights) over time. Each player must then play to maximize his point total at all points of the game, rather than throwing the game or playing kingmaker once winning that individual match becomes unlikely or impossible. This works for all sorts of games where point totals determine that game’s winner. Games without an embedded scoring mechanism (e.g., Diplomacy) likely resort to assigning metagame point values to ranking the finishing position of players. If that gets you turtling you don’t want, you may have to add a scoring metric for offensive successes in games that don’t have it.
Mix in point decay over time to give the historically weaker players a better chance to climb the game standings. For years at WotC, such a scoring system was used to track play across hundreds of games of hearts (or their version of the card game). Last I checked, it was still in use. For the record, my score, if still in their database, was pretty abysmal. My math on when to shoot the moon was more than a bit faulty. Sigh.
Leaving behind analog games, a more modern example can be found in current-gen shooters, in which the player has a persistent account with currency or experience points attached. Earning xp for each kill, or each completed objective, means that play remains fundamentally pure, even in multi-sided contests. This metagame functions more like a true economy instead of just scoring, but it produces the same effect.
Admittedly, the attachment of a persistent metascore can’t help one-off matches with random players at the game store or outside of a persistent social network. Sorry, board game conventions. You’re going to have to rely more on social pressure, or the sorts of rules that Pulsipher adopted.