Introduction to the dilemma of the Prisoner

Manuel de la Herrán Gascón



Before of to begin with the dilemma of the prisoner classic i want to show a varying yet more simple. The following variation of the known dilemma of the prisoner will help to to explain the possibilities of the Artificial Life for the analysis, the simulation and the resolution of problems real.

We suppose a joint of individual; each one of the which possess a determined quantity of money. Each person puede to decide if to invest that money in a certain business, and in the case of to make it, what quantity to invest.

The business in issue is so fabulous that duplicate immediately any investment, but with the peculiarity of that the total of the money resulting (the double of the money invested) is distributed for equal between all the individual, independently of the quantity delivered for each one.

We see the cases extreme. For example, if exist 10 individual and all invest a peseta, the investment of 10 pts will produce other 10 pts of benefit and the result of 20 pts it will be distributed between all, with it that each individual will obtain 2 pts.

If of the 10 individual nobody invest, not there is benefit and all it is maintain as they were. But if only one of they invest a peseta, the peseta it is multiply for two and these two pesetas they will be distributed between the 10, and now all will will have 1,2 pts except the unprepared investing that will will have 0,2 pts

If of the 10 individual, only 5 of they invest the peseta, the result of 10 pts is distributed between the 10, of form that the that not invested will earn a peseta and the that invested it is will remain as they were to the principle.

Each individual does not know always the investments that will make the rest of individual. The objective is to obtain the maximum benefit possible, but each individual it is find then with a great dilemma:

If relies in the kindness of its companions, and suppose that these will accomplish large investments, would have to to invest the minimal quantity possible for to obtain thus the maximum benefits without to risk its money.

Without embargo, the other not they are cloddish, and they will be capable of to arrive to the same conclusion. In that case, if all invest the minimal quantity, the benefit it will be the minimal for all, and the business so fabulous that were having not it will be being of usefulness for nobody.

For so much, it more intelligent seem to collaborate, and to invest all the maximum quantity, for to obtain all the maximum benefit. But, ¿puede one to rely in that the other also it will make?

The individual produces thus a reasoning regulation that it is discussion between the benefit own and the of the group.

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The Dilemma of the Prisoner in the life real

It is puede to think that this is a case artful, without parallelism in the life real. All we know that not exist in the markets of values investments that duplicate its value immediately. Without embargo, yes exist in our world a merchandise whose value it is multiply when it is sum. Is to say, exist something for it that we can to assert that 1 + 1 = 4. Something in it that "The all is more that the sum of the parts"

That "something" is the knowledge. The knowledge is the "money" that the persons they can "to invest" and to obtain multiplied. A person puede to form in a document knowledge that to him there is side months to discover. Other person it will be able in so alone some hours to learn on that topic. Will suffice with to read the document. ¿That would be of the programmers without the manual? There the we have, for thousands, to arrangement of all and independently of if it is there is participated in its draft.

A time inserted in flour, the dilemma of the prisoner it is puede to observe in a imaginary equipment of development computer in the that some posts of work such time disappear if the project fail.

The programmers they can to opt for to conceal its knowledge to the rest, with the intention of to emphasize and to assure its permanency in the company. But if all it is behaved of this form would begin the problems: tasks that it is repeat unnecessarily, mistakes assignments a and other time,... the project it is convert in a chaos and such time nobody preserve its post.

If all shared all its knowledge, the project has more probabilities of success, and it will be more probable that it is maintain all the posts of work. But ¿it is puede to rely in that the other also it will make?

Not exist dilemma when the benefit obtained in the cooperation is very high and the prejudice very under or void.

We suppose that the car of a individual remain jammed in the mud. The alone not puede to move it, but with the it help of other person yes would. The benefit that obtain one of they in the cooperation is very high and the prejudice of the other is very small, hardly a light effort. In these cases, the trend it will be to the cooperation.

Exist other examples. We think in the quantity of persons that it is see involved in the process that empty in that we could to take us a toasted with jam for the tomorrows. Some intervened in the obtainment of flour, other drove the trucks in the that it is transport, other built the highways for the that go the trucks...

Us we give account of that the persons we are all related of some form. Is easy to understand that the specialization in the work is beneficial for the society, and produces a better utilization of the resources.

But not is necessary that a entity superior organize this allotment of tasks. The organization is automatic, is a process that emerge of the interaction of the objective of each individual. Enough that the entities act in its own benefit for that this it is produces. For example, if there is shortage of computer, this will encourage the students, that will fill the classrooms and that demand will remain attended.

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¿For what it is flame "The dilemma of the prisoner"?

The dilemma of the prisoner is a old and known game that it is study in sociology and sciences political. The game consist in it following. Two prisoners of war, enclosed in cells separated in the jails of the enemy, fear for its lives and attempt it be saved it being made to happen for spies of the decree where it is find prisoners, reason that would to explain its clothes and accent.

For it be assured of these affirmations, both go to be interrogated for separated for its jailers. Each one is going to be asked for the identity of the other. Each prisoner puede to opt for "To collaborate" with the other, assuring that there is overdraft that the companion is a spy of the decree opposed and that it is find unjustifiably in the jail. "To collaborate" is to defend to the other. "To defraud" it will be not to make it.

Exist for so much four possibilities, that none defraud, that it make the two, that it make the first or the second.

If... ...then
the player 1... and the player 2... the player 1 receive... and the player 2 receive...
Co-operate Co-operate 3 3
Co-operate Defraud 0 5
Defraud Co-operate 5 0
Defraud Defraud 0 0

Each prisoner receive a premium in function of this table. We suppose that the 0 is the death: one of they will die if the other not to him defend. But in the case of that yes to him defend, the premium received is much greater if to him accuse. Is to say: each one, individually, not obtain no benefit is to collaborate with the other, but depend many of that the other there is decided to collaborate with one same.

This is a game very known, and already it is there is organized before. As it is puede to suppose, for to obtain good results is more appropriate to play with money of truth. Douglas R. Hofstadter comment the results that had the game organized for he, in a varying very similar, in the article "Topics Metamágicos" of the Magazine Investigation and science, August 1983.

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ArtículoHofstadter, Douglas R. "Temas Metamágicos". Revista Investigación y ciencia, Agosto 1983.
LibroDawkins, Richard. 1994. "El gen egoísta". Salvat Ciencia.
ArtículoBass, Thomas A. y Martín, Luna "Por qué ganan los buenos". Revista "Muy Interesante", nº 203, Abril 1998.
ArtículoAxelrod, Robert "La evolución de la cooperación" Alianza Universidad, 1996.

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