Prisoner’s Dilemma

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so. (Wikipedia)


In simple terms, prisoner’s dilemma is a bargaining game where the biggest reward is only achieved when both players co operate, yet they might not do so. There could be various factors involving as to why they don't. One of the factors relates to the behavioral psychology of a person, where his past behavior influences the other's decision. 

For instance, You let your friend borrow your hair dryer few years ago. Even though you guys are relatively close, she hasn't returned your hair dryer. Say, after all these years, she wants to borrow your hair straightener. You will be reluctant to let her borrow your hair straightener or any other item for that matter. In this way, your decision was impacted by learning your past experience with her. This made you uncooperative(defect) to her in letting her borrow your hair straightener.

It was first proposed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker then formalized the game with prison rewards, naming it "Prisoner's dilemma".

Example 1: Partners in crime

Let’s consider an example of something we have witnessed countless times on TV. Michael and David are partners in a “suspected crime” and have been apprehended by the police. They are placed in separate interrogation rooms. Since there is no concrete evidence to convict them, they will only be spending a year in jail, unless, one of them confesses the crime and testifies against the other.

The detective involved in the case interrogated two partners separately, offering them both a same deal. Each of the individual have an option to confess having committed the crime with the other person, or to deny having committed the crime.

Conditions

If Michael confesses having committed the crime while David denies, Michael will only receive a year of imprisonment while David receives a 10-year sentence. Again, if Michael and David both confess having committed the crime with each other, they each receive 3 years of imprisonment. However, if both of them deny having committed the crime, the police have no option but to let them serve their 2 years sentence each due to the lack of evidence.

In the other room, David is offered a same deal and has to go through the same decision matrix. It is in David’s best interest, like Michael, to plead guilty and testify against Michael, or he could be serving 10 years in prison while Michael only serves a year before he walks out a free man.

The Result

Both individuals plead guilty to having committed the crime. As a result, they both serve 3-year sentence by cooperating, while they could have remained silent and served 2 years each. Both had the opportunity to testify against one another or stay loyal, and with the fear of receiving the maximum sentence, they both chose the safer option.

A true Prisoner’s dilemma is carried out only once, but if they are played out repeatedly using the same participants, the term is now referred to as Iterated Prisoner’s Dilemma.

Example 2: Pricing war

Another example for the prisoner’s dilemma can be understood by taking into account the pricing war between two different companies for a similar product, say a tube of toothpaste. If both companies try to undermine the other to dominate the market, they might lose the profit value for the product. However, if both the companies decide on a single price, then they can share the market and not lose their profit value for the product.

Observations

This form of cooperation in order to receive the best possible outcome is referred to as beneficial cooperation. In the Example 1, beneficial cooperation would be for Michael and David to stay silent and only receive a 1 year sentence. The manner in which two parties try to protect themselves at other’s expense is referred to as defection. In other words, defection is not cooperating.

The general idea is that cooperation is better than defection, as it’s the base of human kindness. Think about all the movies where two lead actors are imprisoned, we are always hoping for them to cooperate. The idea that defection is morally bad isn’t always true.

There are both ups and downs to cooperation and defection. If you’ve watched any mafia movies ever, most are based on reality, you’ll see how easily gangsters can commit crimes in broad daylight and not be apprehended for it, because of the cooperation between the mafia and the police. This is one of the major reasons why gang violence hasn’t been put to full stop despite unlimited amount of resources.

There are plenty of other examples of how prisoner’s dilemma can occur in our daily lives. Often times, we end up with a shorter stick due to the lack of cooperation with our colleagues or partners.

Bottomline, depending on the circumstances, both cooperation and defection can be good.

A popular quote by an 18th century French Novelist is quite relatable in the context of perceiving cooperation and defection in Prisoner’s Dilemma.

There is no truth. There is only perception.