Interdependence.
from "How Real is Real?" by Paul Watzlawick.
The Prisoner's Dilemma.
The concept of interdependence is perhaps best introduced by the game-theoretical model of the Prisoner's Dilemma, formulated and named by Albert W. Tucker, a professor of mathematics at Princeton.
In its original version, a district attorney is holding two men suspected of armed robbery. There is not enough evidence to take the case to court, so he has the two men brought to his office. He tells them that in order to have them convicted he needs a confession; without one he can charge them only with illegal possession of firearms, which carries a penalty of six months in jail. If they both confess, he promises them the minimum sentence for armed robbery, which is two years. If, however, only one confesses, he will be considered state witness and go free, while the other will get twenty years, the maximum sentence. Then, without giving them a chance to arrive at a joint decision, he has them locked up in separate cells from which they cannot communicate with each other.
Under these circumstances, what should they do?
The answer seems simple: since half a year in prison is by far the lesser evil, it makes sense for them not to confess. But no sooner have they reached this conclusion in the solitude of their separate cells than a doubt arises in their minds: "What if my companion, who is bound to conclude correctly that this is what I am thinking, takes advantage of the situation and confesses? Then he goes scot-free and I get twenty years. On second thought, I am safer if I confess. Then, if he does not confess, I am the one who goes free."
But immediately, a new realization presents itself: "If I do this, I not only betray his trust in me to make the decision most advantageous for BOTH of us (i.e., not to confess and get away with six months), but if he is as trustworthy as this would make me, he will arrive at exactly the same conclusion. We will both confess and be sentenced to two years -- a far worse outcome than the six months we could get if we both denied the crime."
This is their dilemma, and it has no solution.
Even if the prisoners somehow succeeded in communicating with each other and reach a joint decision, their fate will still depend on whether each feels he can trust the other to stick to the decision -- if not, the vicious circle will start all over again. And on further thought each will invariably realize that the trustworthiness of the other depends largely on how trustworthy he appears TO the other, which in turn is determined by the degree of trust each of them has FOR the other -- and so forth ad infinitum.
There is a vast literature about this particular pattern of interaction, the most authoritative work probably still being Anatol Rapoport and Albert M. Chammah's book [with Carol J. Orwant, "Prisoner's Dilemma: A Study in Conflict and Cooperation", Univ. of Michigan Press, 1965)].
An excellent, very concise summary of the nature of the Prisoner's dilemma, its relation to such extrarational notions as trust and solidarity, and its place in modern mathematical thought can be found in a recent article by Rapoport in Scientific American ["Escape from Paradox" Scientific American, 217:50-56 (July 1967)]
The Prisoner's Dilemma is usually presented in the form of a 4-cell matrix, based on the assumption that there are only two players, A and B, who both have two choices each, namely a1 and a2 for player A, and b1 and b2 for player B.
The figure on page 100 is such a matrix and shows simply that if A chooses a1 and B chooses b1, they will win 5 points each. If B chooses alternative b2 instead, A will lose five points and B will win eight. The opposite happens if their choice is a2, b1. Finally, if the outcome is a2, b2, they lose three points each. These payoffs are known to both players.
Since the rules of the game are that the choices must be made simultaneously and without the possibility of communicating with the other player in order to reach an agreement (which the other player could, of course, break at any round of the game), this simple mathematical model contains in itself the essence and the hopelessness of the Prisoner's Dilemma, as the reader can easily convince himself by playing it with another person --- preferably not a friend.
Actual situations of the Prisoner's Dilemma type are far more frequent than one might expect. They arise whenever two or more people are in a state of disinformation as a result of having to reach a joint decision about which, for one reason or another, they cannot communicate.
In human relations, especially marriages, communication is usually quite possible, yet partners may be living in a chronic Prisoner's Dilemma situation if they do not trust each other enough to choose the alternatives most advantageous to BOTH of them. ***
In terms of the Prisoner's Dilemma matrix, they realize that the most reasonable and jointly desirable decision would be a1, b1, which offers both of them a comfortable gain. But as we have seen, this decision can be reached only through mutual trust; in the absence of such trust the only "safe" decision is a2, b2, which amounts to a joint life of quiet desperation.
....
pages 98 to 102.
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