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Cooperative Negotiation & The Prisoner’s Dilemma

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Albert W. Tucker (1905 – 1995), one-time Chair of the Mathematics Department at Princeton University, made famous “the prisoner’s dilemma” as an example of a non-zero-sum situation. This “game” is frequently used to illustrate points in economics, math, philosophy (especially in the realm of decision theory), and, as used here, in negotiation. A quick internet search will reveal innumerable versions of the game online, along with a great variety of explanations and set-ups.

No matter how well one does one’s homework, in negotiation situations one never knows for certain how the opponent will act. Here’s one way a prisoner’s dilemma scenario can be put together:

EXAMPLE: You and a friend, Xeno, are arrested by the police and charged with a crime. If you both stay silent, you will each be held partially responsible and sentenced to two years in jail. If you each confess, you will each get four years in jail. If one confesses and implicates the other, who stays silent, the confessor will go free and the implicated party will spend eight years in jail.

The number of years in jail varies among different formulations, and in many cases this is played as a multiple-round game. That is, each person decides to speak or stay silent, penalties are assessed, and then each decides anew, with the penalties from each round accruing until the game ends.

We could represent the above single-round prisoner’s dilemma as follows: