The Prisoners Dilemma

It is worth talking about game theory, for a moment; if anything just to clear up any misconception let us take a look brief look game theory.  Game theory has actually very little to do with Gamification or game design in fact, it is about mathematical modeling that is used to predict outcomes “on the actions of more than one agent, as well as perhaps on other facts about the world. Game Theory is the study of what rational agents do in such situations.”(Weatherson, 2011).  Myerson (1991) defines game theory as the “study of strategic decision making. More formally, it is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.”

One of the most famous models that is often used is what is commonly referred to as the prisoners dilemma.  As you can see from the matrix below we have two men, both have been apprehended by the police.  If both remain silent (game theory calls this cooperation), they will only receive a one year jail sentence each.  Both are offered a chance to confess and send the other player to jail for 20 years (game theory calls this defection from a cooperative relationship).  If both players cooperate they would receive the best outcome, however, both are thinking that if they turn on each other, they may not do jail time and therefore will defect and confess to the crime.

PD Matrix

Fig, 1: The Prisoners Dilemma shown as a martix

Theorists tell us that the criminals will always confess as they will only act in their own self-interest, therefore leading them to both go to jail for 5 years.

This is the prisoner’s dilemma. Game theorists have determined that confessing is always the answer for both parties in this case. The reason for this is that each party must assume that the other will act with only self-interest in mind.   By listing the preferences of the choices we can predict what the criminals will do.

  1. 20 year term
  2. 5 year term
  3. 1 Year Term
  4. Get out of Jail free

PD Preferences

Fig, 2: The Preference Matrix of the Prisoners Dilemma

Looking at Player 1’s preferences in the first column we can see that the 5 year term is preferable over a 20 year term if he does not confess (2 is great than 1).  In Column 2 we can see that see that not going to jail is better than going to jail for 1 year, therefore, the best strategy is to confess no matter what his partner this does is called the dominant action. The prisoner’s dilemma is the simplest of the game theory models, as we add more variables and players the mathematics become much more complicated.

References:

Myerson, R. B. (1991). ‘Game Theory: Analysis of Conflict, Harvard University Press, p. 1. Chapter-preview links, pp.vii – xi

Weatherson, B. (2011) ‘Lecture notes on game theory.’ [Online]. Available at: http://brian.weatherson.org/StA-GameTheoryNotes.pdf (Accessed: October 17, 2013)

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