Prisoner’s Dilemma in Breaking Bad
The prisoner’s dilemma is an oft-studied example of game theory and strategy in social situations. The classical example involves two prisoners who have the options of confessing or keeping silent. While both prisoners are better off keeping silent, the dominant strategy and Nash equilibrium is for both of the prisoners to defect. An example payoff matrix might look like this:
where the numbers refers to years spent in prison. There are, however, a number of assumptions we place in this game: prisoners aren’t allowed to communicate, prisoners don’t hold any loyalty to each other (if they did, this would modify the payoffs of confessing), and that this is a one-shot game- there aren’t any opportunities for interaction between the prisoners or future retribution after the conclusion of the game.
Breaking Bad is (or more accurately, was) a critically acclaimed and highly successful television series detailing the story of a meth king pin. A number of elements from game theory are applicable throughout the series, including its own version of the prisoner’s dilemma. In the episode “Hazard Pay”, 9 former (low-ranking) employees with knowledge of the protagonist’s involvement have been arrested on lesser charges and incarcerated in hopes they will reveal information on both each other their former higher-ups. The DEA offers each of them the classical dilemma deal- confess on the others and receive reduced sentences, or keep silent and hope the others don’t confess their own involvement.
The first assumption needed for this game to work (no contact between prisoners) are only loosely kept- prisoners aren’t allowed contact with each other (as they are separated by different sections and facilities), but are all represented by the same lawyer who is able to relay information to them. The second assumption is broken (inability for outside reward/retribution) as each of the prisoners are compensated “hazard pay” for their silence. In addition, each prisoner is highly aware that to confess invites danger upon themselves and their families, as the previous enforcer of the operation has not been incarcerated. Thus the payoff for the prisoners might look something like this:
where there exists positive payoffs from keeping silent (receiving compensation) and reduced payoffs for confessing (external threats, loss of pay). Although there is no dominant strategy in the way this game is set up, the mixed equilibrium leads to keeping silent being the most probably option played.
However, in the later episode “Gliding Over All”, the means for distributing “hazard pay” is halted by the DEA and the previous enforcer killed. With the removal of outside rewards and retributions, the situation more closely fits the model of the prisoner’s dilemma, with payoffs similar to the first matrix. This is later demonstrated to be true as we witness one prisoner attempt to strike a plea bargain with the DEA. The protagonist is also aware of this strategy as well- in the time it takes the DEA to find the prisoner willing to sell information at the lowest price (reflecting the concepts of markets and auctions in class), he has all of them murdered before they can reveal anything.
Sources:
Both episodes are available online (but on a subscription basis). The free synopses can be read at:
http://breakingbad.wikia.com/wiki/Hazard_Pay
http://breakingbad.wikia.com/wiki/Gliding_Over_All
In addition, this website discussed other elements of game theory throughout the show:
http://www.overthinkingit.com/2012/07/16/breaking-bad-prisoners-dilemma/