From: John Conover <john@email.johncon.com>
Subject: Re: Slinky
Date: Wed, 22 Mar 95 00:24 PST
MKTGGURU writes:
> Wrong again moose breath. The sailor chased a slinky up the stairs and a
> marine dropped his spring.
> Hasn't this been a wonderful day- filled with those events that alter
> and illuminate our times. Thanks for being there John
This will be lengthy. But let me make a point. Consider the following
"game." It is, although simple in operation, a rather complex game,
and I will wade through the optimal logic. The rules, of this very
simplified rendition, of the "game" is as follows:
There are two players, and each player has only two choices for
each iteration of the "game," and those choices are to chose
either "A" or "B." If both players pick "A," then each wins 3
dollars. If one picks "A," and the other "B," then the player
picking "B" wins 6 dollars, and the other player gets
nothing. However, if both players pick "B," then both win 1
dollar.
Or, to put it in clear, concise form, the payoff matrix would look
like:
Player One
A B
+-----+-----+
A | 3,3 | 6,0 |
Player two +-----+-----+
B | 6,0 | 1,1 |
+-----+-----+
This "game" is what is known to game theorists as the "classic
iterated prisoner's dilemma." The choice "A" is known as a
"cooperation strategy," and the choice "B" is known as the "defection
strategy" for each player. It is a very subtile and devious game. Here
is why, and the logic you would go through. Just before you played,
you would think:
1) If I pick "A," there are two possible scenarios:
a) If he picks "A," I would get 3 dollars, and he would get 3
dollars.
b) If he picks "B," I would get 1 dollar, and he would get 6
dollars.
2) If I pick "B," there are also two possible scenarios:
a) If he picks "A," I would get 6 dollars, and he would get
nothing.
b) If he picks "B," I would get one dollar, and he would get
one dollar.
Note that by picking "A," the best you could do is to win 3 dollars,
and the worst is to win nothing. But, by picking "B," the best you
could make is 6 dollars, and the worst is one dollar. It would appear,
at least initially, that "B," is the best choice.
But, here is where it gets subtile. You opponent, unless he is stupid,
(correction, "Thinking Challenged," in politically correct
vernacular,) will determine exactly the same thing, and will never
play "A." So you both make one dollar every time you play the "game."
But you could make 3 dollars-if you cooperated, by both playing "A."
But if you do that, there is an incentive for either player to play
"B," if he knows the other player is going to play "A," and thus make
6 dollars. And we are right back where we started. Indeed, a very
complex game.
As a simple, empirical, application of the "game," consider the case
of marital dilemma:
Suppose that marital bliss is upset by a grouchy mate that just
happens to get up on the wrong side of the bed, (ie., the mate is
playing a defection strategy-you were playing a cooperation
strategy, in the interest of preserving the marital bliss.) What
do you do? You get grumpy right back, right? And, when the mate
"comes around," and starts cooperating, you start cooperating, and
marital bliss is restored. It turns out that this "tit-for-tat"
strategy is one of the most effective known, and has been recorded
as a political solution to many dilemmas throughout history, (like
a "tooth-for-tooth" statement in the Old Testament-there are
similar statements in Zen, Hinduism, etc.)
This is a key point. Some games have explicit solutions. Most don't,
and will require a strategy, like "tit-for-tat." (There are other
solutions, and other variants of this "game" that are far more
sophisticated.) How do you separate the "games" into those that have
explicit solutions, and those, like the iterated prisoner's dilemma
that don't? It turns out that, 1) there must be an incentive to play
the cooperation strategy, and 2) there must be a larger incentive to
play the defection strategy, ie., most political situations. For
example, it is in a nation's interest to have the largest nuclear
stockpile. Naturally, if all nations adopt the defection strategy, we
have a prescription for the nuclear arms race. So, we have
international conferences, that "equalize" the destructive power of
consenting nations (cooperation strategy,) which is immediately broken
by China, Israel, Iraq, etc., (defection strategy.)
So, was the nuclear arms race rational and logical? That depends on
your point of view, but in a strict, logical sense, yes it was. It
was a rational, logical strategic solution to the iterated prisoner's
dilemma "game." We have to be very carful about making statements that
politics is irrational, when it apparently it has a formal, logical
basis.
Note that all wars in recorded history have been fought to resolve a
question of authority, ie., two players, booth choosing a defection
strategy. (Note that if only one player choose a defection strategy,
and the other one chose a cooperation strategy, there would have been
no war-and one less nation.)
It should be clear that politics is an essential ingredient of
civilization, if not its defining attribute, (the Greeks considered
"man the political animal,") and is the dynamic operation of
cooperation and defection strategies between players. Politics and
conflict are inevitable, and unavoidable.
One of the poets in Oruk, the first city in civilization (circa
3000BC, in what is now Iraq,) telling the story of how the gods
delivered civilization to man:
"I give you civilization. It will contain farming, commerce, and
prosperity. But it will also contain war and greed. And you must
either take it in whole, or nothing. And once taken, it can never
be given back."
The rudiments of game-theory are not new.
John
References:
For "light" reading, see "Prisoner's Dilemma", William Poundstone,
Doubleday, "New York, New York", 1992.
For more rigor, see "Games and Decisions", R. Duncan Luce and Howard
Raiffa, John Wiley & Sons, New York, New York, 1957.
--
John Conover, john@email.johncon.com, http://www.johncon.com/