Prisoner`s Dilemma

The Prisoner´s dilemma was first formalized and discussed by Meryll Flood and Melvin Dresher (1950). The story behind it is explained as follow:

Two people committed a crime together. Isolated from each other, both are interrogated by the prosecutor. Both have the possibility either to confess or to deny the crime. The penalty of both people will dependent on their own decision, as well as on the decision of the other person. If both deny the crime, both will get a small penalty. If both confess the crime, both will get a medium penalty. If one denies and the other confesses the crime, the person who denies will get a high penalty while the person who confesses gets no penalty.

Albert W. Tucker formalized the dilemma. One main result is the following pay-off-matrix:

1

P(x) is the penalty of person x

with g<h<i<j as the numbers of years in prison

 

To make it more obvious let the penalties (in years) be g=0, h=1, i=3, j=10, what leads us to matrix

2

Obviously both people are in a dilemma now. The goal of their decision could either be minimizing their own penalty, or the sum of the penalties, or a mixture of the two.

If person A wants to minimize the sum of both penalties, for sure the best solution is that both people deny. But without knowledge of person B’s decision, it would be very risky for A to deny. If B confesses while A denies, A will get a penalty of 10 years and the sum of penalties would be 10 years, too. Furthermore, Player A knows that he will get a maximum of 3 years in prison, if he decides to confess.

If person A wants to minimize his own penalty, the desirable solution is that person A confesses while person B denies, because this would result in 0 years for player A. The risk, if Player B decides to confess too, is now not that high. In this case person A would get 3 years.

In mathematical game-theory this situation leads to the Nash-equilibrium[1]. Both people will confess and get a penalty of each 3 years. This result is surprising, because a solution exists, where both people would get a lower penalty, while the sum of penalties is lower, too. The solution of the Nash-equilibrium is not optimal (in the sense of Pareto (1848-1923)).

But how to reach this optimum in sense of Pareto[i], if the cognitive solution leads into Nash-equilibrium and fails? To get closer to the optimal solution, we must ask ourselves: which reasons are influencing the decisions of both players?

On a first step, this decision depends on the objectives of the players. Do they try to minimize their own penalty or the sum of penalties or a mixture of both? In other words: Do they make their decisions based on egoistic or altruistic motives? Furthermore, the degree of the players’ risk-aversion is influencing their decisions. Both traits (the degree of altruism as well as the degree of risk aversion) are used in the field of trait models of emotional intelligence.

On a second step, the decisions of the players will depend on their estimate of the opponent’s decision. Variables for this estimation are questions like: How egoistic/altruistic is the opponent in general? How much does the opponent care about the other player in person? How much does a player trust the opponent? In which emotional mode is the opponent in the moment of decision? Or more generally: How knowledgeable are the players of the other person involved? All these variables describe emotional abilities as used in the field of ability models in emotional intelligence.

But, as the player’s make decisions inside ‘the prisoner’s dilemma’, if their motives are based on emotional intelligence, probably the solution will be (at least) touched by emotional intelligence, too. Maybe a pure cognitive solution does not even exist?

Forward-looking to praxis in youth work:

The objective of the praxis part related to this article will be to transform the basic model of the prisoner’s dilemma into a game based on rewards instead of punishments. Furthermore, it makes sense to develop modus for a game over many rounds. This would give an insight, if the decisions of the players would change, if they e.g. gain trust caused by previous decisions of the opponents, or make different decisions based on the opponent in person.

[i] A solution is pareto-optimal, if it is not possible to improve the situation of one subject without worsening the situation of another.

John Forbes Nash. “Non-cooperative games.”, Princeton University (1950)

@Nils Leichsenring

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