Shall we talk about other multiplayer games in which everyone playing is supposed to be playing for themselves to win?

That's right: Poker!
Casinos will not let known married couples play at the same table. That doesn't stop any other type of conspiracy from happening, nor would it stop a married couple from pretending to not be married while playing. So, my buddy with two pair whom I've signalled that I have a full house decides to bet. Everyone but me and one other player folds. This other player calls my buddy or raises, it doesn't matter. If he raises, I raise. If he calls, I raise. No matter what happens, my buddy raises on his turn even though he knows I have him beat because of my earlier signal. Now the hapless third guy is stuck again and can call or raise but we'll do the same thing again. Depending on the rules of the game there'll be a limit on the number of raises or eventually one of us three will have all of our money in and the betting will be over. If my full house is the winning hand (Almost a certainty if you know Poker, though I have lost with it before), my buddy will lose and the other guy does too. Had my buddy folded his bad hand at the beginning, the pot would have a lot less money in it and the betting round would've stopped the moment my opponent called me.

Another type of Poker conspiracy is called, "Playing soft". In this ploy, you bet light against your buddy and play hard against the rest. Almost the same thing.

In both these ruses, the players will divide up their winnings away from the table and of course if it's just the two of them against each other for the pot they can bet in whatever way they think appropriate to cover for what they're doing to everyone else at the table.

And then there's cheating, but that's a whole different can of worms.

Also, there's the game that got me to stop playing games of this nature, though I still play Poker. I play Poker with people I know and we have the rule that married couples can only have one of them at the table at a time. Generally though, the wives stay out of the game and let us knucklehead men play our Poker. Brothers seem to make good opponents in Poker. :) Perhaps it's the money and the brotherly competitiveness. Who can say, but there's nothing like telling your brother to put all his chips in if he wants to see your hand. Playing Poker with strangers is always fraught with conspiracies and the danger of cheats, but it's a fun game just like Run Around the Pond is a fun game.

Anyways, that other game is: Risk!
For those unfamiliar with this game, it's easy to understand. You win the game by conquering the world! At the start of the game the world is divided up amongst all the players and everyone gets an army. From the very start the politics of the game happen. Conspiracies aren't even concealed. One player might tell another that if he attacks me he'll leave him alone. At any time time in this game any one person can be ganged up on and forced out even if it causes those attacking that person to lose the game on a later turn. (That sounds familiar, doesn't it). Arguments happen even if everyone plays for themselves trying to win because the strategy of winning the game itself is complicated. (Dang, this sure sounds like Run Around the Pond). So you have people pointing fingers and name calling each other because of a perceived idiotic play or lack there of. How I missed the simularities of Risk and Run Around the Pond is beyond me, but perhaps it is because I haven't played Risk! in over twenty years and it's hard to imagine ducks quaking in the water as having anything remotely simular to armies, conquest, and world domination.

After coming to blows with a friend of mine while playing a game of Risk! over twenty years ago, I decided to never play it again if there were more than two people involved. Soon afterward I thought of playing four handed but with two players on a team. If you have to attack your partner to achieve a goal, that's just how it is. Playing this way eliminates the conspiracy problem and still retains all the other things about Risk that make it a fun game. I think this would also work for Run Around the Ponds and that was why I requested it in the previous post. Teams would be a lot of fun and the strategy seems like it'd be just as tough as it is now. Maybe not, but I suppose the game would have to played as teams first to see if it would be a good one to play it or not.