People often speak of the fabled zero-sum game, where there is one winner and one loser of equal balance; the winner gains +1 util, and the loser -1 util. This is incredibly unlikely. One common example is sportsball games, in which one team wins, one loses, end story. But if that was the end of the story, almost no one would bother to play sportsball. The worst teams would have tremendous negative utility, and so would simply not play; that would make the teams that were going to (just barely) beat them the new worst teams, repeat until out of teams. All games would be between two teams that believe that they are actually best, and one of the teams would be wrong. This is only a stable dynamic over multiple contests if 50% of the teams are delusional.

Sportsball games are all in reality positive-sum games, in which the players gain utility from playing, from fame, from exercise and social interactions and lucrative contracts. Zero-sum games are generally bad, dumb games to involve yourself in, and so you generally don't.

Just as zero-sum games are not profitable, negative-sum games are worse. They happen, as wars exemplify, but they are not as common as people might think.

Enter variable-sum games. This is where most of game theory and human interaction takes place. In these games there is some sort of negotiation or compromise such that all parties involved can come to an accommodation... or, alternatively not. The simple example is selling apples to your neighbors. If you sell the apples cheaply, you gain less and your neighbors gain more; if you sell the apples for a lot, you can make much money, but your neighbor buys fewer apples. If you shoot your neighbor in an apple-pricing dispute, they are dead, and then you are in prison. There are many paths to different outcomes covering a range of positive- and negative- (and maybe even zero-)sum outcomes.

Variable-sum games include normal people things like buying and selling and weird game-theorist-type things like the prisoner's dilemma. The optimal solution in variable-sum games is known as the Nash equilibrium, and the applied solution as economics.

Variable-sum games are perhaps most noteworthy in that maximizing all outcomes across participants almost universally comes from clear communication between players, maximizing knowledge of relevant information, the ability to build and enforce trust, and network effects; but outcomes for any given individual benefit from an imbalance in these factors. Thus, much of the interactions individual agents undertake in the real world involve unclear communication, hiding information, avoiding effective contracts, and cutting out competitors and/or alternative resources.

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