In class, Mr. Stewart introduced something called the prisoner's dilemma. This is a famous example of game theory in which two prisoners face two possible choices: to cooperate with each other and deny committing any crime, or to defect to the police and confess to the crime.
The picture depicts this situation. There are two prisoners, A and B, and the matrix represents all of the possible combinations of denial and confession. The years refer to the length of the jail sentence each prisoner will get based on their decision.
The best choice for the two prisoners collectively is for both of them to cooperate. If they are able to get together beforehand, they could collude with each other to decide on this optimal strategy. (In the real world, law enforcement has realized this collusion could happen, so they generally don't let suspects strategize together.)
However, just like the collusion that happens with oligopolies, there is still the incentive to cheat: if Prisoner B betrays the collusive deal and defects, then A will get 10 years but B will go free, which is an even more attractive option to B than going to jail for just 1 year.
Thus, even if the criminals get together beforehand, if each prisoner is "playing not to lose," (which is instinctively what humans do), then both prisoners will confess and betray each other. This means that they will achieve a sub-optimal result: both will serve for 5 years in jail instead of 1 year each.
Though individual criminals want to defect to avoid the harshest penalty (10 years), that is not the case when it comes to organized crime (I will use the Mafia as an example, but this pattern occurs in basically all crime organizations). If two Mafiosos defect and both of them serve 5 years, that means the Mafia just lost 10 years worth of labor AND the defectors might spill secrets that could hurt the Mafia even more!
That's where the famous saying comes into play: "snitches get stitches." It's pretty self-explanatory, but, to discourage people from ratting out the Mafia to law enforcement, anyone who confesses to law enforcement will be punished very harshly.
From an economic standpoint, this introduces new incentives for the prisoners. Let's re-examine this new matrix.
If the prisoners deny the crime (which is what the Mafia wants), they still have the same possible outcomes of serving 1 or 10 years. But if they defect, their options change: they can either serve 0 or 5 years, but either way, the Mafia will kill them. This gives the prisoners only one way to stay alive: deny the crime and protect the Mafia.
Just as with most things in economics, the prisoner's dilemma can get complicated in the real world. The first basic example is complicated by the behavior of organized crime groups, and even with their policy of "snitches get stitches," the existence of witness protection further complicates things. But understanding the strategies of prisoners, the Mafia, and law enforcement can still be aided with game theory.
Great post Anya! You did a really good job of explaining game theory and clarifying the example from class. I think that this example of game theory also helps to illustrate the concept of collusion and why it is illegal. I think that this game theory type matrix can be applied to the costs of producing certain products and in oligopolies collusion could help these companies increase their profit margin without lowering prices, harming the consumer.
ReplyDeleteAnya, I thought your post was very unique, and an incredible example of applying economic theory to real life. It goes back to how economic theory is often predicated on two assumptions: that all other things are held equal, and that human beings are rationale. The introduction of the mafia is an example of an inequality in the equation, and so despite the logical results of the prisoner's dilemma, there is an illogical possible result: death. One would think that jail time means protection, at least from outside decisions, but because of criminal organizations, this is just not true. The rational decision then changes from avoiding sentencing to avoiding death. I think your post is an example of how economic theory is sometimes difficult to translate to real-world applications. That idea that all other things are held equal is fantastic for theories, but in real-world it is frequently not applicable. Organizations and individuals have dozens, if not hundreds of factors influencing their decisions, just as the prisoners not only have prison time but also retribution from the mafia to consider when deciding to confess or not. So, I guess decisions in economics aren't as easy as we think they are. Thank you for a great post, Anya.
ReplyDeleteThank you Anya for giving a very thorough explanation of the game theory! Firms, like these prisoners, can sometimes struggle to find a dominant strategy. Usually what happens is both companies/prisoners will gravitate towards the option that is the safest; in this case, that is confessing. In some cases, the players in game theory might have better options by deviating from the initial strategy. In other cases, the player has no incentive to switch the strategy: this is called Nash equilibrium. So, in the case of the prisoner's dilemma, the Nash equilibrium is for both players to betray each other.
ReplyDeleteThe prisoners dilemma is one of the best real world examples of game theory. For the prisoner, they have can take the risk of confession either resulting in freedom or a long sentence. They also have the choice of denial resulting in a small sentence or a very long sentence. If we look at these risks, we can analyze which may be the best choice. No matter what, denial results in jail time. Jail time could be short, but also has an equal chance of being very long. Confession has the possibility of freedom, or a medium jail time. Looking at it this way, I find confession to be the best way. I feel that if every prisoner would just study economics, they can greatly increase the chance of making the right choice!
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