Prisoner's Dilemma

by Anatol Rapoport, Albert M. Chammah

The term "Prisoner's Dilemma" comes from the original anecdote used to illustrate this game of strategy. Two prisoners, held incommunicado, are charged with the same crime. They can be convicted only if either confesses. If both prisoners confess, their payoff is minus one. If neither confesses, it is plus one. If only one confesses, he is set free for having turned state's evidence and is given a reward of plus two to boot. The prisoner who holds out is convicted on the strength of the other's testimony and is given a more severe sentence than if he had confessed. His payoff is minus two. It is in the interest of each to confess no matter what the other does, but it is in their collective interest to hold out.



There is no satisfactory solution to the paradox of this game. Its simplicity is misleading. What seems rational from your own point of view, turns out to be detrimental in the end.



This book is an account of many experiments in which Prisoner's Dilemma was played. Analyzing the results, one can learn how people are motivated to trust or distrust their partners, to keep faith or to betray, to be guided by joint or selfish interest. The method represents an important step toward building a bridge between psychology which is based on hard data and reproducible experiments and psychology which is concerned with internal conflict.

270 pages, Paperback

First published December 15, 1965

Reviews

[Tom Schulte · Rating 3 out of 5]

This is a mathematics analysis of a psychological study of men and women undergoing a series of Prisoner's Dilemma games. Touching on the importance of the costs/benefits for Cooperate (C) or Defect (D), this is a good model of basic statistical analysis of similar studies, let along of the specific application of game theory.

...
3. The correlation coefficient p_C1C2 over a population of pairs. This is a grosser measure than the p_i; it measures the overall similarity of pair members with respect to their cooperative frequencies.

4. The response-conditioned propensities E, n. 5, and w Of these and we are measures of responsiveness to the other's choices, while and are measures of response to one's own choices. (N.B.: the two pairs are not in- dependent since one's own choices always occur in conjunction with the other's choices [cf. p. 68].)

5. The state-conditioned propensities x, y, z, and w. These are propensities similar to the preceding ones but now separated by reference to the four mutually exclusive response categories. It will be useful also to compare x, y, 1-2, and 1 w (cf. p. 84), which are measures of persistence in the same response in each of the four states.

What is really fascinating is the concluding analysis on male-female differences in recurring strategies after series of games. I wonder if I can find any contemporary reviews.. I think these conclusions could popularly be seen as controversial as The Bell Curve: Intelligence and Class Structure in American Life, or something.

( "A simple learning model (called PAVLOV)" and laboratory experiments with human subjects support two conditional strategies, state-conditioned (PAVLOV) and response-conditioned (TIT FOR TAT).).

...we see that men playing men are somewhat more likely to respond cooperatively to the other's cooperative choice than to retaliate against the other's defecting choice... However, women playing against women are much more likely to retaliate against the other's defecting response than to respond cooperatively against the other's cooperative response... When men play against women, the retaliating tendency is slightly greater than cooperative responsiveness in both...

...the women's propensities are brought up when they play against men, the men's propensities are brought down when they play against women. When men play against women, the propensities are practically equal when averaged over the entire session.

Comparing with & we see that men playing men are somewhat more likely to respond cooperatively to the other's cooperative choice than to retaliate against the other's defecting choice... However, women playing against women are much more likely to retaliate against the other's defecting response than to respond cooperatively against the other's cooperative response... When men play against women, the retaliating tendency is slightly greater than cooperative responsiveness in both.

Next we examine the correlation measures. The p's of the men (playing against men) are consistently higher than those of the women (playing against women), which is to say that the men tend to imitate each other more than the women. The values of the p's in the mixed groups indicate that there men tend to imitate women more than women tend to imitate men... In short, men are inclined to play tit-for-tat more than women...

...the value of P in the mixed groups is again intermediate between that in the male and in the female pairs. With respect to p however, the tendency to become like each other is strongest in the mixed groups We shall not venture to interpret this result.

Next we look at the dynamics of the state-conditioned propensities. We have already seen (cf. Chapter 11) that the mean probability of continuing a given state is not necessarily a constant (as implied by the four-state Markov model) but appears to be a function of the number of times the state in question has just occurred. In particular, we conjecture that the lock- in effect is due primarily to the fact that the more times in succession the CC or the DD state occurs, the more likely it is to be repeated at least in the pairs in whose protocols sufficiently long runs occur. This effect, if it occurs, is shown in columns 22 through 25. Comparing the probabilities of the continuation of CC runs, we see that in the male pairs these steadily increase and that the increase is still seen even when the pairs without runs longer than three plays are included. In the female pairs this effect is not observed. Even in the pairs where CC runs at least five plays long occur, ree actually declines. This is to say, when women play women the average probability of a CC response following two consecutive CC's is actually less than the average probability of a CC response fol- lowing a single CC. This indicates that the lock-in effect on CC does not operate in the average female pair. In mixed pairs, the lock-in effect is observed in pairs containing CC runs of at least five. It is still ob- served when pairs with runs not longer than four are included and is lost when pairs are included which contain no runs longer than three. With regard to DD runs, the picture is reversed.

...

In the male pairs, the lock-in effect is observed only in the selected pairs with DD runs at least five long, is lost as soon as pairs with no runs longer than four are included, and is actually reversed when pairs with runs no longer than three are included. In the female pairs, on the other hand, the effect is observed even when pairs with runs no longer than three are included. The mixed pairs behave like the male pairs with respect to the DD runs. We conjecture that women be- come more prone than men to lock-in on DD as a DD run continues.

...the woman is somewhat less prone to switch from successful defection to cooperation, both tendencies being a reflection of man's greater propensity to give tit-for-tat.

Turning to the final lock-ins..., we see that seventy percent of the male pairs end the sessions locked in, and that of these over four times as many pairs have locked in on CC than on DD. Of the female pairs less than fifty percent end the sessions locked in and of these almost twice as many have locked in on DD than on CC. The mixed pairs are

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[Mathew Vicknair · Rating 2 out of 5]

This book gives a decent analysis of Prisoner's Dilemma but there is a heavy reliance on jargon. Best read after appropriate college level classes are taken (psychology and economics) because this book attempts to be very scholarly, which actually hurts its readability, even if you understand it.