Economics is all about making choices.
Usually, the tendency is to think of economics as being about unemployment, and inflation rates, and the stock market. But these things are a reflection of the choices we make about who provides what products and services, and how much of each should be made available, and who gets to consume them.
As individuals and as a society, we are constantly making choices because we are limited in what we can do. There are only so many hours in a day, only so many skills that can be learned, only so many experiences to be sampled. So, at its core, economics is the science of making choices.
An increasingly fertile approach to understanding how people make choices and what optimal choices can be made is found in the study of game theory. And one of the more interesting and deceptively complex games is the Prisoner’s Dilemma.
Introduced by Merrill Flood and Melvin Dresher in 1950, with polish and the name added by Albert Tucker in the same year, the Prisoner’s Dilemma (PD) is an example of a game where an individual making choices based on his own rational best-interest may actually hurt himself in the long run.
The narrative behind the game is usually quite simple and a little dull, so what I present here has been dramatized a bit to add flavor. It is based on the introduction to the PD found in Principles of Economics: Economics and the Economy, Version 2.0 by Timothy Taylor.
Two known felons, call them Al and Bob, have just knocked over a liquor store and have made off with $5000. They jump in their old beater of a car and rush from the scene of the crime. As they barrel down the city streets they run a red light, smash into the back of car, and flee on foot with the money. Owing to their bad luck, a police prowl car was nearby and the officers begin to chase them. Al and Bob duck into an alley where they toss the money in a sewer drain minutes before they are apprehended by the cops. As the police are charging these two with hit-and-run and reading them their Miranda rights, the radio starts blasting out an APB describing two men wanted in the liquor store hold-up. Since Al and Bob match the description, the officers haul them to the police station where each is held separately until they can appear in a line-up. Unfortunately, the store owner is unable to positively identify either of them and, hoping to loosen their tongues so that they would confess, the police try the following tactic.
Keeping Al and Bob in separate rooms, unable to communicate with each other, the police send in one of their toughest cops, Detective Taylor. Taylor confronts Al first and lets him know that the police have him dead-to-rights on the liquor store caper and on the hit-and-run and that, all told, Al is facing 8 years of hard time. Al spits back that all the police have on him is the hit-and-run and he can do the 2-year stint in the county jail (seems Al has been down this road before, if you’ll forgive the pun). Smiling, Taylor tells Al that Bob is making a deal and, in return for him naming Al as the mastermind behind the robbery, Bob’s going to get out in 1 year while Al does the full 8-years. Taylor urges Al to not be a sap and to confess. He tells Al that if he owns up to his crime and implicates Bob as his accomplice, the DA will cut his prison time and send both him and Bob to jail for 5 years. Taylor says he’ll give Al twenty minutes to think it over and he leaves the room, ostensibly to let Al sweat but really to make the same speech to Bob.
Having been in and out of police stations, court rooms and jails most of his adult life, Al recognizes that the only hard evidence the police have is that Al and Bob were involved in a hit-and-run. The police are probably not even sure who was driving. So if he keeps his mouth shut they can’t touch him on the liquor store robbery. However, he also recognizes that if Bob bites on the deal, there will be enough evidence to convict him of both crimes. He also knows that Bob is reasoning the same way.
Okay, what should Al or Bob do? They choices are summarized in the following table.
| Bob | |||
|---|---|---|---|
| Remain Silent | Confess | ||
| Al | Remain Silent | 2 years for Al 2 years for Bob |
8 years for Al 1 year for Bob |
| Confess | 1 year for Al 8 year for Bob |
5 years for Al 5 years for Bob |
|
Clearly, if Al is looking out for his own interests, then the best deal he can make is if he betrays his partner, confesses his involvement, and Bob stays quiet, through either a sense of loyalty or a gamble that Al is staying quiet too. However, Bob will be pursuing his own interests and he is also likely to confess, betraying Al in the same fashion.
Here is the Prisoner’s Dilemma in all its glory. It is an example of a social dilemma where one-sided betrayal gives the best results for the betrayer but in which cooperation gives the best results for the group as a whole (cooperation gives 4 years total compared with 9 and 10 years for the one-sided and two-sided betrayal scenarios, respectively).
Of course, the story of Al and Bob is contrived, but it contains key elements of real social dilemmas that affect us all. And, in fact, the PD has been widely studied and applied in diverse areas such as biology, psychology, sports, and diplomacy. Any situation where the payoff for cooperation is less than the payoff for one-side betrayal usually presents this situation. Mathematically, this amounts to any situation where the table above can be translated into
| B | |||
|---|---|---|---|
| Cooperate | Betray | ||
| A | Cooperate | C for A C for B |
S for A L for B |
| Betray | L for A S for B |
M for A M for B |
|
where the largest payoff (L) > cooperative payoff (C) > mutually-betrayed payoff (M) > sap payoff (S).
One real world example of this is the OPEC oil cartel. Each member of the cartel has entered into an agreement with the others to hold production to a particular quota so that each can reap sizable profits. Each nation also knows that, without warning, one member could either raise production or lower price to boost its earnings – thus betraying the others. Also, each nation knows that, if two or more of them engage in this behavior, then they all suffer. Each of us is involved in this game, since oil prices affect prices for all the goods and services we consume.
Another, and perhaps more important, example of the Prisoner’s Dilemma is the situation of the Free Rider problem discussed last week in the context of the Plymouth Colony. As a citizen in Plymouth Colony, my cooperative payoff (C) is an ample ration of food that the Colony provides, which is made up of some of the food I diligently grew on my farm along with some of the food my neighbors also diligently grew on theirs. My sap payoff (S) is a smaller ration of food that results when some of my neighbors shirk their responsibility and grow little or no food and my contribution has to be stretched over more mouths. My largest payoff (L) is a ration of the same size as I got for (S) but this time, since I am the one who grew nothing, I am effectively getting free food. Since I didn’t have to work for it and, indeed, I may not be working at all, I can eat well on the smaller ration as long as other people are the saps. Finally, my mutual-betrayal payoff (M) is a tiny ration, not enough for me to avoid chronic hunger. It results from most or all of the Plymouth citizens basically betraying each other.
During the years 1621-22, the Plymouth Colony actually engaged (without knowing it explicitly) in a real life Prisoner’s Dilemma with real life consequences. Many of them died and all went at least a year and a half barely surviving. They resolved the Prisoner’s Dilemma by eliminating the cooperate box and making all property private. This eliminated the Free Rider problem and resulted in a bountiful feast in the autumn of 1623.