Historical footnotes to game theory
[ by Charles Cameron — philosophy, psychology, history, game theory, dilemma, commons cooperation, analogy, 9/11 ]
I have an interest in game theory that is much like my interest in music: I can’t play, but I can whistle. And so it is that I’ve substituted curiosity about the history of the thing, and whatever analogical patterns I can discern there, for any actual ability at the thing itself.
Somewhere in my analogy-collector’s mind, then, I have these two quotes, cut from the living tissue of their writer’s thoughts, and prepped fpor contemplation. I find them, in retrospect, quite remarkable.
Jean-Jacques Rousseau, in On the Inequality among Mankind, wrote:
Such was the manner in which men might have insensibly acquired some gross idea of their mutual engagements and the advantage of fulfilling them, but this only as far as their present and sensible interest required; for as to foresight they were utter strangers to it, and far from troubling their heads about a distant futurity, they scarce thought of the day following. Was a deer to be taken? Every one saw that to succeed he must faithfully stand to his post; but suppose a hare to have slipped by within reach of any one of them, it is not to be doubted but he pursued it without scruple, and when he had seized his prey never reproached himself with having made his companions miss theirs.
And David Hume, in A Treatise of Human Nature:
Your corn is ripe today; mine will be so tomorrow. ‘Tis profitable for us both that I shou’d labour with you today, and that you shou’d aid me tomorrow. I have no kindness for you, and know that you have as little for me. I will not, therefore, take any pains on your account; and should I labour with you on my account, I know I shou’d be disappointed, and that I shou’d in vain depend upon your gratitude. Here then I leave you to labour alone: You treat me in the same manner. The seasons change; and both of us lose our harvests for want of mutual confidence and security.
Those two, I believe, are fairly well known – I was delighted the other day to run across a third sample for my collection. William James, in The Will to Believe, writes:
Wherever a desired result is achieved by the co-operation of many independent persons, its existence as a fact is a pure consequence of the precursive faith in one another of those immediately concerned. A government, an army, a commercial system, a ship, a college, an athletic team, all exist on this condition, without which not only is nothing achieved, but nothing is even attempted. A whole train of passengers (individually brave enough) will be looted by a few highwaymen, simply because the latter can count on one another, while each passenger fears that if he makes a movement of resistance, he will be shot before any one else backs him up. If we believed that the whole car-full would rise at once with us, we should each severally rise, and train-robbing would never even be attempted.
The first two quotes are of interest as showing the forms that an idea which will later be mathematized can take. They are, if you like, precursors of game theoretic constructs, although neither Hume nor Rousseau appears to be mentioned in von Neumann and Morgenstern‘s Theory of Games and Economic Behavior.
The third, I think, is even more interesting.. Consider the eerie and heroic “fulfillment” of that third paragraph if read “as prophecy” – in this account from the 9/11 Commission Report of the events on United Flight 93:
During at least five of the passengers’ phone calls, information was shared about the attacks that had occurred earlier that morning at the World Trade Center. Five calls described the intent of passengers and surviving crew members to revolt against the hijackers. According to one call, they voted on whether to rush the terrorists in an attempt to retake the plane. They decided, and acted. At 9:57, the passenger assault began. Several passengers had terminated phone calls with loved ones in order to join the revolt. One of the callers ended her message as follows:
“Everyone’s running up to first class. I’ve got to go. Bye.” The cockpit voice recorder captured the sounds of the passenger assault muffled by the intervening cockpit door.
Yesterday’s highwayman is today’s hijacker, yesterday’s train is today’s plane…
If there’s anything to be learned here, it’s not a novel way of protecting trains or aircraft from passengers of malicious intent —
It’s that there’s a subtle thread running from something akin to instinct that’s also close to unspoken common sense, surfacing for a moment in the writings of thoughtful individuals, leading on occasion to the formulation of exact mathematical principles — but also (i) available, (ii) in the human repertoire, (iii) to be acted upon, (iv) cooperatively, (v) as required, (vi) via the medium of human common interest, (vii) which provides the resultant trust.
Which may in turn offer some reason for hope — for a humanity in various forms of communal distress…
August 22nd, 2011 at 2:46 am
Charles: I had this post on Flight 93, which may be on point and of interest.
August 22nd, 2011 at 4:42 am
For the sake of those readers who don’t click through and read Lex’s post, and for my own convenience in retrieving it, here’s what I take to be the money quote:
The general rule that Lex derives is instructive, too:
But do read the whole post.
August 23rd, 2011 at 12:59 am
This is excellent. I’ve been grazing through von Neumann and Morgenstern’s book for the last several weeks. Found it as a result of Wylie’s book on strategy.
Also, while I have a William James volume on my shelves, I’ve not had time to read. I told a colleague at lunch today that I’ll not be reviewing any books in the coming weeks because everything I’m reading is old. I reread for a second time this year, Powis Smith’s excellent treatment of The Origin and History of Hebrew Law (1931)—not sure what I was thinking the first time through—as I found a couple of quotes suitable for my book! I call these literary odds and ends:))
August 23rd, 2011 at 3:41 am
If you can graze through vonN & M — you’re a better man that I am, Gunda Din! : )
The best I can do is consult the index, and then point at it.
August 23rd, 2011 at 6:56 pm
Been thinking about your response…for me grazing is wandering into the midst of dense stuff I barely understand, and straining to make meaning. By no means did I intend to convey expertise or anything beyond novice familiarity…this is one of those books I handle, not able to make sense of most of it, but gathering enough to be rewarding—or more often, confounded:)))
August 23rd, 2011 at 8:18 pm
I wrote a piece about just this approach a while back — High Conceptual Thinkers. Yup, I’m that way with von Neumann too! [vbg]
August 23rd, 2011 at 8:45 pm
I remember that piece, but had forgotten my comment on Hayek—since adding that comment, I’ve returned to Hayek a couple of times. Everything I’m presently reading is old—although a new little book called Genius arrived today and I may have to make some room:))