Siegfried, Tom. "3 Nash’s Equilibrium--Game theory’s foundation." A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature. Washington, DC: The National Academies Press, 2006.
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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
nology) in Pittsburgh, his choice for major had become chemical engineering. He soon switched to chemistry, but that didn’t last, either. Finding no joy in manipulating laboratory apparatus, Nash turned to math, where he excelled.
He first mixed math with economics while taking an undergraduate course at Carnegie Tech in international economics. In that class Nash conceived the idea for a paper on what came to be called the “bargaining problem.” As later observers noted, it was a paper obviously written by a teenager—not because it was intellectually naive, but because the bargaining he considered was over things like balls, bats, and pocket knives. Nevertheless the mathematical principles involved were clearly relevant to more sophisticated economic situations.
When Nash arrived at Princeton in 1948, it had already become game theory’s world capital. Von Neumann was at the Institute for Advanced Study, just a mile from the university, and Morgenstern was in the Princeton economics department. And at the university math department, a cadre of young game theory enthusiasts had begun exploring the new von Neumann– Morgenstern continent in earnest. Nash himself attended a game theory seminar led by Albert W. Tucker (but also explored game theory’s implications on his own).
Shortly after his arrival, Nash realized that his undergraduate ideas about the “bargaining problem” represented a major new game theory insight. He prepared a paper for publication (with assistance from von Neumann and Morgenstern, who “gave helpful advice as to the presentation”).
“Bargaining” represents a different form of game theory in which the players share some common concerns. Unlike the two-person zero-sum game, in which the loser loses what the winner wins, a bargaining game offers possible benefits to both sides. In this “cooperative” game theory, the goal is for all players to do the best they can, but not necessarily at the expense of the others. In a good bargain, both sides gain. A typical real-life bargaining situation would be negotiations between a corporation and a labor union.