[mises] praxeology and game theory
Pro-Choice
David_Heinrich at urmc.rochester.edu
Wed May 19 20:18:25 PDT 2004
Today, in Managerial Economics, the professor talked about Game
Theory. The subject made me hark back to "Austrian Economics and Game
Theory: a Stocktaking" at http://tinyurl.com/2vyna. I also thought of
*The Games Economists Play*, by Murphy, at http://tinyurl.com/2vgoq.
I see some interesting elements of value in game theory.
Fundamentally, it appears to be strongly influenced by praxeology,
human action, as is indicated in the basic Prisoner's Dilemna.
Furthermore, though Murphy notes that game theory has been used to
justify state intervention (because the Nash-equilibrium is not the
optimum cooperation), there are also those who have used game theory
to argue against State intervention. See *The Possibility of
Cooperation* by Michael Taylor.
Anyways, a cruel alternative to prisoner's dilemna occured to me in
the class. This was not really my own creation, but I remembered it
from Baldur's Gate II.
* If both push their buttons, both die.
* If neither push their buttons, both die.
* If one of them pushes their button, but the other doesn't, the one
who did not push the button dies.
* Each of them has one hour to decide whether or not to push the button
* Neither of them can see whether the other is about to or has pushed
his or her button
Obviously, this is a one-shot "game", so we need not considder
repeated games. The following outcome table emerges (in each cell, the
first listed outcome is what happens to A, the second listed one is
what happens to B, given the inputs, which are the row and column headers:
A
---------------------------------------------
| | Push | Don't Push |
|-------------|------------|----------------|
| Push | D,D | D,L |
B |-------------|------------|----------------|
| Don't Push | L,D | D,D |
---------------------------------------------
(clearly, this is a game that you don't want to play)
At first, it appears that there are only three possible outcomes (I
will not differentiate between them both dying from them both pushing,
or them both dying from them both not pushing):
D,D: A dies, B dies
D,L: A dies, B lives
L,D: A lives, B dies
--------------------------
The Game Theorist Analysis
--------------------------
The game theorist analysis, I would guess, would go as follows. A
would prefer that A lives, B that B lives.
A's analysis of the situation would go something like this: If A does
not push the button, A will most certainly die, whether B pushes the
button or not. However, if A pushes the button, he will live if B does
not push the button, though he will die if B also pushes the button.
It is at least conceivable to A -- albeit unlikely -- that if he
pushes the button, he will survive.
B's analysis proceeds in exactly the same manner.
Thus, if each wishes for himself to live, both A and B will push the
button. The Nash equilibrium is that they would both push the button,
and thus that they should both die. In short, if they each picks the
strategy that they see as allowing for the possibility that
their-selves could live, they both will die. According to this
standard line of game theory reasoning, it is impossible that either
of them could live.
--------------------------------------------------
Possible Psychological Ordinal Preference-Rankings
--------------------------------------------------
In the following, I will list possible ordinal preference rankings for
A and B in a list, with the most preferred outcome at the top of the
list, progressively going towards less preferred outcomes. This seems
to be simple, but in fact the list becomes rather long once you
realize that it is perfeclty *possible* that A could prefer D,D, or
that A could be indifferent between the three outcomes, or between two
ofthe outcomes. In the case where there is indifference between two or
three outcomes, they are listed side-by-side
In the case where A is indifferent between two or three outcomes, that
indifference cannot explain why he either pushes a button or does not
push a button. I am aware that preference can only be revealed through
action, and that indifference *cannot* be illustrated by action. These
ordinal preferences I am listing are not all praxeological
preferences, because action can only illustrate preference, not
indifference. They are, rather, preferences from a prior psychological
point of view. Praxeological ordinal rankings can only be revealed via
action.
This is an exhaustive list of all possible ordinal rankings. If I am
either A or B, I know which ranking I prefer:
1 2 3 4 5 6
D,L D,L L,D L,D D,D D,D
L,D D,D D,D D,L D,L L,D
D,D L,D D,L D,D L,D D,L
7 8 9
D,L L,D D,D
L,D D,D D,D D,L D,L L,D
10 11 12
L,D D,D D,D D,L D,L L,D
D,L L,D D,D
13
D,D D,L L,D
Immediately, a problem with game-theory is apparent. It goes beyond
economics and into psychology. From all I've heard, game theory seems
to concern itself only with one possibility: A would want to live, and
B would want to live. This cannot be an acceptable assumption.
--------------------------------------------------
Possible Psychological Ordinal Preference-Rankings
--------------------------------------------------
>From a praxeologically significant standpoint, ordinal preference
rankings can only be revealed through action. However, in this case,
it can only be deduced what one *does not* prefer based on one's
button pushing:
If A pushes the button, what can we deduce? Not much, unless we make
certain assumptions. Strictly speaking, if A pushes the button, all
that we can deduce is that his highest valued outcome was *not* D,L --
that he dies and B lives. There are two possible reasons why A pushed
the button: (1) he preferred that both of them should die (D,D); or
(2) he preferred that he should live and B should die (L,D).
Thus, from the following actions by A or B, in this case, we can only
deduce what they do not prefer:
A pushes button: Does not prefer D,L
A does not push button: Does not prefer L,D
B pushes button: Does not prefer L,D
B does not push button: Does not prefer D,L
---------------------------------
Some Problems with Game Theorists
---------------------------------
It seems to me that game theorists -- not game theory itself -- have
some problems from the start. Namely, they go beyond economics and
into psychology, making assumptions which can hardly be assumed to be
univeral. The game theorist would assume that A would want the L,D
outcome and B would want the D,L outcome. However, why does that need
to be so?
Let's consider one possible preference which everyone seems to reject
off-hand: D,D. Let's say that A and B were married. It is possible to
think that both, then, would place the highest value on outcome D,D,
as both know that neither would want to live without the other.
Once we accept that the fact that it is possible that A and B may have
any of the listed 13 value scales, the normal game theory analysis is
completely exploded, and this seemingly "simple" example becomes
unbelievably complex.
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----- End forwarded message -----
--
Churchill, Winston Leonard Spencer --On the eve of Britain's entry
into World War II:
"If you will not fight for right when you can easily win
without bloodshed; if you will not fight when your victory will be
sure and not too costly; you may come to the moment when you will
have to fight with all odds against you and only a precarious
chance of survival. There may be even a worse fate. You may have
to fight when there is no hope of victory, because it is better to
perish than to live as slaves.
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