Is there anyone among you who has never heard of it? The prisoner’s dilemma (Gefangenendilemma) as a central component of the Game Theory (Spieltheorie)?
For those who do not know what it is about, here is a short description of the so-called cover story:
Two gangsters (G1 and G2) committed a crime together. They can, however, hot be proved guilty of the crime itself. But some smaller offenses can be pinned to them. Now they are isolated from each other. Both prisoners are offered the same thing:
They can either
admit to the crime and incriminate the partner in doing so
or
deny it.
The admission may eventually mean that the “chief witness” goes home free, but only if his partner denies. Said partner will then get five years for lying. If both admit, both get four years (reduction by one year because of the admission). If both deny, the crime cannot be pinned to them. Both will then get one year because of the minor offenses.
There are four alternatives:
1. G1 admits, G2 denies: G1 = 0, G2 = – 5, G1 + G2 = – 5
(The one who admitted as chief witness will walk free, the one who denied will get five)
2. G1 denies, G2 denies: G1 = -1, G2 = -1, G1 + G2 = – 2
(Both deny, nobody can prove them guilty, both get one year in jail because of minor offenses)
3. G1 admits, G2 admits: G1 = -4, G2 = -4, G1 + G2 = -8
(Since both parties admit, they both get four years, which means one year less because of being penitent)
4. G1 denies, G2 admits: G1 = -5, G2 = -0, G1 + G2 = -5
(Same as 1., but the other way around)
Since, in game theory, you usually calculate with gains (profit) but years in jail are not really gains, I gave those years a negative algebraic sign. Consequently, the profit can be written as the positive difference between, for instance, -2 on -5, which equals +3.
I must admit that I am not really a fan of game theory in general and the prisoner’s dilemma in particular.
The entire affair is a nice example from the year 1950. Basically, it only shows that sometimes different decisions might make sense, dependent on whether the interests are egotistical or mutual. In my opinion, that is not quite enough “central content of a theory”. Here are some more
weaknesses of the model:
- You can take random numbers, and the effects will be just as random.
- The cover story is artificially constructed and oversimplifies a highly complex situation. Consequently, you can interpret all manner of things into it. All of those are hugely dependent on social situations and personal structures.
- Difficult decisions, and here particularly the ethical ones, can never be generalized.
- Every individual situation differs from the next. There is no measurable objectivity.
- The probabilities of a decision are never taken into consideration, yet they are always intuitively there (gangster’s honour, consequences of the wrong decision,…).
- Taking the example of the prisoner’s dilemma, just imagine how the discussion would change if the death penalty were the maximum penalty in the model. That would leave room for plenty of speculation. And besides, I really cannot imagine how such a situation might be objectively simulated in a field test.
- For instance, if you attempt to give the prisoner’s dilemma general validity by changing the cover story, you will notice that it cannot be done. You can see it best in an entirely neutral model: two creatures have to decide pro or con totally independent from each other. For the consequences, the success measurements are a for pro against con and vice versa. You get b for both pro instances and c for both con. And the probability that the other party will decide pro or con is appropriated as 50%, or at another value. Using this kind of model, you can easily build up both theories that make sense and theories that do not. And then you can experimentally prove all manner of things.
From a scientific point of view, the prisoner’s dilemma, along with the entire game theory, is probably useless both mathematically and sociologically. Not to mention the economical usefulness, which today is always at the forefront.
RMD
P.S.
🙂 As you can see, I am not really very much in favour of the game theory. Incidentally, the same is true of Operation Research, Profiling or NLP for humans. I tend to get sick in my stomach easily when confronted with them. To me, they often seem like “scientific esoteric” with a high potential for danger in various directions. Therefore, I intend to write a few more articles on game theory. You might call them “criticism of game theory”. The game theory is defined both as part of mathematics (Mathematik) and sociology (Soziologie). And it seems to me that it is just not really possible to combine the two areas.
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