|NONZERO THE LOGIC OF HUMAN DESTINY By ROBERT WRIGHT|
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PART I: A BRIEF HISTORY OF HUMANKIND
PART II: A BRIEF HISTORY OF ORGANIC LIFE
PART III: FROM HERE TO ETERNITY
Some game theorists, such as Thomas Schelling, frown on the "negative-sum/positive-sum" distinction. The reason is that they frown on the "zero-sum/non-zero-sum" terminology to begin with. What is commonly called a "zero-sum" game they would rather call a "fixed-sum" game. After all, if the winner of a tennis match gets $100 and the loser $50, that is not, strictly speaking, "zero-sum," but it has the essential property we mean to imply with the term "zero-sum"; the two players' interests are wholly at odds, and good news for one equals bad news for the other. And the source of this property is not that the sum of the benefits they get from playing the game is zero—which it isn't—but that the sum of the benefits is "fixed," in this case at $150. By the same token, what is commonly called a "non-zero-sum" game Schelling would rather call a "variable-sum" game (to describe, say, the dynamic between two teammates in a doubles match that pays $100 to the winning team and $50 to the losing team).
Schelling is surely right that a zero-sum game is merely a special case of a fixed-sum game—the case in which the sum is fixed at zero. So the "fixed-sum/variable-sum" terminology is, strictly speaking, more generally applicable to life. But "zero-sum/non-zero-sum" is the terminology used by the founders of game theory, John von Neumann and Oskar Morgenstern, and it remains in common use. And its implication that there are negative-sum and positive-sum games—though slippery on close inspection—is useful for present purposes.
For more on game theory—including the classic game "the prisoner's dilemma," and its use in computer simulations of evolving cooperation—click here.