The Prisoners' Dilemma

 

What is The Prisoners Dilemma?

It is a hypothetical situation ( of a game analysed in game theory) which shows that two rational individuals might not cooperate even when it is in their best interest to do so. Here,  two prisoners Jack and Jill are arrested for a minor crime and believed to have committed a major crime. Both are detained in separate holding rooms and questioned. They have 4 possible options:

·       Admit that your partner committed the crime and you can go free. The partner would get 3 years in prison.

·       If you stay silent and the partner says you did the crime, you get 3 years and the partner goes free.

·       If both stay silent, they will both get one year in prison each for the minor crime.

·       If they both betray each other, they will both get two years each in prison.

Basically, each of them can do one of two things: stay silent or betray. Staying silent would be cooperating while betraying would be defecting.

What should they ideally do? Looking at it from Jill’s perspective, if she thinks Jack will stay silent, she should betray as then she will go free. If she thinks Jack will betray, she should definitely betray as otherwise she will get 3 yrs and Jack will go free. Jack will think exactly the same thing. Ideally, they should have both cooperated but the safer option when they don’t know what the other will do is to defect. Hence, most likely that both will defect to save themselves.

In real life marketing examples, let’s say that two cola companies Happy Cola and Joyous Cola are deciding how much to spend on their advertising campaign. Since both their products are identical, advertising would make a considerable difference to their sales. Lets imagine that they have to choose between advertising a lot or not at all. Also to simplify further, lets imagine there are a total of 100 customers who would drink cola. If both don’t advertise, then by random chance, 50 people would select Happy cola while 50 would select Joyous Cola. At £2 a can, they would each make £100. Lets say advertising costs £30. If Happy Cola advertises and Joyous Cola does not, then 80 people will buy Happy Cola and 20 will buy Joyous Cola. Happy Cola will spend £30 on advertising, after which it will make £130.

80 cans of Happy Cola X £2 -£30 =  £130

Joyous Cola will make:

20 cans of Joyous Cola X £2 = £40

 

If they both advertise, again half will buy Happy Cola and half will buy Joyous Cola. Each will make :

50 cans of Cola X £2 - £30 = £70

Results are similar to the Prisoner’s dilemma. Both cooperating and not advertising is the most preferable situation but both know that advertising will make more money for them. Unlike the prisoners though, these Cola companies can talk to each other and influence decisions.

 The label ‘Prisoner’s dilemma’ is given to situations where even though two entities could benefit from cooperating or suffer losses by not doing so, they still find it difficult or expensive to coordinate their strategies.

Defection always results in a better payoff than cooperation, when we don’t know the competitor’s choice, it is a dominant strategy. The only result from which both players could only do worse by unilaterally changing strategy is mutual defection. Thus, it is the only strong John Nash equilibrium in the game. Hence, cooperating mutually yields a better outcome than defecting mutually but it is rarely the rational outcome as one is always hesitant to cooperate as one is looking out for one’s self interest. This is counter intuitive, really.