Video Excerpt

IRV
How was someone like Barankin on the West Coast able to find out what was going on with George Dantzig on the East Coast?

PHIL
Barankin received his bachelor's from Princeton and maintained Princeton connections. He was pretty well acquainted with George Dantzig and Albert Tucker and a number of other figures in the field.

I don't know what started him off on linear programming, but he was doing work in mathematics and taught a couple of courses in the Berkeley mathematics department.

One was on convex cone sets and functions. My friend, Dean Gillette, and I both enrolled as students of his. Dean did a very nice thesis in recursive games, games whose play is followed by one of a number of other games.

I chose to study zero-sum, two-person games of perfect information. All Von Neumann-Morgenstern games have stop rules that terminate play, and those games are shown to be strictly determined in pure strategies:each player has an optimal pure strategy with a guaranteed payoff.

My background was in more abstract mathematics and set theory. I proposed the question, "What happens if the game had no stop rule?" I suppose you can play a game infinitely long. A referee would have to decide who won when he saw this infinite sequence of moves. As far as set theory goes, that's not a problem.

I set out to investigate games of perfect information of infinite length. My thesis advisor was pretty sour about that. He didn't like the theory of games much, anyway. He had some objections to the Von Neumann and Morgenstern theory of utility; he felt it was much too cramped and rigid to be a useful model of social behavior.

Anyway, I posed the question, got some preliminary results, and showed using a fair amount of set theory that games of infinite length and perfect information were not strictly determined, unlike games of finite length. If I knew what your plan was, then I could win. And if you knew my plan, you could win, even though the games were supposedly of perfect information.

I proved it using the axiom of choice. As it turned out, the proposition itself was more or less equivalent to the hypothesis of the continuum. It's way out there.

But I proceeded to the point of also looking for subclasses of games that would have a value in the Von Neumann and Morgenstern sense. Got a number of results.

Then sometime in 1953, I was startled to read a paper published by David Gale and a student of his in which they laid out the foundations of the theory I was working on. I thought I was scooped, until I realized that they said, "Here's an interesting open question." I had already answered that open question, so Barankin had to agree that my thesis was publishable.

Previous

Next