My Faults My Own

One's ponens is another's tollens.

John Nash, 1928-2015

CNN | Mathematician John Nash, wife killed in car crash

John Forbes Nash Jr., the Princeton University mathematician whose life inspired the film A Beautiful Mind, and his wife died in a car crash Saturday, according to New Jersey State Police.

Well, okay, somehow the fact that his life inspired a Hollywood film made it into the obit before the fact that he won the 1994 Nobel Prize in Economics. (Note: "Nash called the film an 'artistic' interpretation based on his life of how mental illness could evolve -- one that did not 'describe accurately' the nature of his delusions or treatment.") But in actuality, it's enormously difficult to describe the impact that this man had on the field of Game Theory, which now underlies much of economics, politics, and has even been applied to describe the strategy of penalty shootouts in soccer (where it closely predicts the strategies that top players actually use).

And if you're anything like me, you'll find his 1950 dissertation a refreshing respite from page after page of obituary:

Non-Cooperative Games (typewriter facsimile)

Introduction

Von Neumann and Morgenstern have developed a very fruitful theory of two-person zero-sum games in their book Theory of Games and Economic Behavior. This book also contains a theory of n-person games of a type which we would call cooperative. This theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game.

Our theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others.

The notion of an equilibrium point is the basic ingredient in our theory. This notion yields a generalization of the concept of the solution of a two-person zero-sum game. It turns out that the set of equilibrium points of a two-person zero-sum game is simply the set of all pairs of opposing "good strategies."

In the immediately following sections we shall define equilibrium points and prove that a finite non-cooperative game always has at least one equilibrium point. We shall also introduce the notions of solvability and strong solvability of a non-cooperative game and prove a theorem on the geometrical structure of the set of equilibrium points of a solvable game.

As an example of the application of our theory we include a solution of a simplified three-person poker game. (...)

It was one of the first -- and certainly not the last -- paper he'd write in the field, but oh, what a seminal one. And as a last tidbit:

He so impressed one professor that his letter of recommendation for Princeton had just one line: "This man is a genius."

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