One of the most popular thought experiments for economists and psychologists is the Prisoners' Dilemma. This one experiment can serve as a metaphor for many other things, including morality in general. The game works like this. You and a partner commit a crime, and are caught. The police believe you are the culprits but have difficulty gathering persuasive evidence. The evidence against you is weak, and so to increase their leverage the police put you both in separate rooms and make you each a separate offer.
They want you to confess to the crime and rat-out your partner. If you confess and your partner does not, you are given only 1 year in jail while your partner receives 4. Your partner is given the same offer, and if she confesses but you don't she gets only 1 year and you get 4. If you both take the deal and confess, however, you each get 2 years in jail. If neither takes the offer and you both remain silent, you each get 3 years in jail. Remember, you are both in separate rooms and cannot communicate. Moreover, there was no way for either of you to expect this offer and prepare in advance for it.
When economists think about what players might and should do, they are participating in the field of economics called game theory. When economists have people participate in games like these (modified versions, of course, where prison time is changed to money) and collect data on how people behave, they are mixing game theory with the field called behavioral economics, where they document how people actually "behave."
Figure 1—Prisoners' Dilemmaprisoner dilemma better.jpg)
Game Theory: Dominant Strategy Equilibrium
It is easy to develop a logical prediction of what each prisoner will decide. Think about what is best for you, if you were one of the prisoners. What happens if the other prisoner confesses? You are better off confessing then, for 3 years in jail is better than 4. What if the other prisoner doesn't confess? You are still better off confessing, as you will receive 1 year of prison instead of 3.
| and the other confesses | and the other doesn't confess | |
| If you do not confess | you get 4 years | you get 3 years |
| If you confess | you get 3 years | you get 1 year |
So no matter what the other prisoner does, you are better off confessing. You should therefore be unconcerned with what the other prisoner might do because you are always better off confessing. Because confessing is the best strategy regardless of what the other Prisoner does, it is referred to as a dominant strategy.
The other prisoner faces the same dilemma, so confessing is a dominant strategy for her also. It is only sensible that each person will follow their dominant strategy, and so both players should confess, causing both of them to receive 3 years of prison. This is the Dominant Strategy Equilibrium, where each person pursues their dominant strategy and each get 3 years of prison.
I got mine, Jack!
But wait! You say. If they both confess they receive 3 years, compared to only 2 years if they do not confess. Why would they willingly confess, then? The reason is that they are making this decision separately, without any ability to talk to the other person, mutually decide on the best strategy for both, and enforce the agreement. If they could make an enforceable decision together, of course they would not confess, but that isn't the Prisoner's Dilemma, and it is for that very reason the police separated the prisoners to begin with.
So the prisoners do what is best for them, and following their individual interest and not the group interest, they are not as well-off as they could be. This is a reoccuring theme in economics. There are many instances where societies can improve themselves by working together, but the incentives that exist cause people to look out only for themselves. Consider voting. Voting is stupid, from a certain point-of-view. You are more likely to get hit by a car on the way to the polling location than you are to influence the election results. If you cared only about your narrow self-interest, no rational person would vote. Yet we also know that if nobody votes democracy doesn't work, and a horrible government will result.
Often the only way to do what is rational for the group is to do what is irrational for oneself. That is why we vote, why we tips waiters we will never see again, and try to live by the Golden Rule. Being kind to strangers you will never again encounter is irrational for you, but absolutely necessary for a harmonious society.
A Metaphor for Society
The Prisoners' Dilemma game so fascinates economists because it is a metaphor for social life in general. Throughout the day we are kind to other people even at an immediate cost to ourselves. Every favor and kind gesture takes time and resources away from ourselves, yet it doesn't feel much like a cost, does it? We are not playing the Prisoners' Dilemma game with each other, even though we must decide the extent to which we work with and against others all the time. The game must be altered before it truly represents our social life. The prisoners only play the game once, be we interact with the same people over and over throughout our lives, and if we acted in our immediate self-interest we are not acting in our long-term best interest.
You are dining with a friend. You are both done eating and the check has arrived. You crudely announce that you are not paying one dime, and leave. There is no need to worry about the waiter chasing you out of the restaurant, for you know your "friend" is a sucker and will pay the bill to avoid an embarrassing argument with the restaurant. You filled your stomach for free, with no immediate consequences. What you did is perfectly rational, in the immediate sense.
This story is absurd because no one does this, and no one does this because we know that if we alienate those around us we will forever be labeled an asshole, and no one will want to work with us, do us a favor, or even consider a proposition. What we are playing is something like the Prisoners' Dilemma game, except that it is played repeatedly, and between the same two prisoners.
Cooperate, Cooperate: This repeating game is depicted below, where the numbers now represent benefits as positive numbers and costs as negative numbers. When we cooperate with other people and they return the notion, both benefit (by 2). You take your friend's kids to school when they are busy, because that friend will eventually return the favor. Let's not just look at hypothetical examples. Consider the Yanomamo people of the Amazon, where various primitive tribes live near one another in the rainforest. These are a fierce people who become respected by their tribes only by killing others. In order to be victory in battle the tribes need strong alliances, and they establish these bonds through formal rituals. After meeting at an established location, one tribe performs a fierce dance with weapons around the other tribe, showing they could kill the other tribe but decide not to. The other tribe then does the same. This rite then unites the tribes, allowing them to cooperate with each other for mutual benefit.(F1) These mutual benefits are reflected in the gain of "2" which each cooperating tribe receives.
Video 1—A Glance at the Yanomamo Tribes and Rituals
Betray, Betray: The Yanomamo develop understandings of cooperation with other tribe largely so they can fight and kill other tribes. You join with a nearby tribe and form a united attack on a tribe downstead. That tribe then establishes alliances on their own so they can better fend off these attacks. Moreover, every death must be revenged. You killed their men, and you can expect them to kill some of yours. The reciprocating back-and-forth of murder and murder represents a losing situation on both sides.(F1) There are some individuals who might temporarily gain from an attack, and perhaps a few cheftians who maintain their power by encouraging these attacks. Overall, though, everyone loses when two sides battle without end. This is represented by the -2 accrued to both when both betray each other.
Figure 2—Metaphor for Society metaphor for life.jpg)
Cooperate, Betray: Then there is the possibility that one side will attempt to cooperate, finding itself betrayed by the other. Remember the formal rituals the Yanomamo use to establish alliances. Your tribe visits another tribe on the pretense of seeking an alliance. The other tribe puts down their weapons so that your tribe can exhibit exhibit your war dance, weapons in hand. The other side demonstrates their willingness to align themselves with you, which is why they sit weaponless before you. You didn't really come to make friends though. At the end of your dance when you are supposed to put down your weapons and let the other tribe dance, you kill the vulnerable tribe. They sought to cooperate, while you sought to betray. You easily annihilate the other side, taking all their women and possession. You receive benefits of 4, and they pay costs of 4.
Cooperate, Betray: Let's play again. The Yanomamo don't just battle once and call it quits. They have probably been doing this for thousands (tends of thousands?) of years. The two tribes that unite and continually cooperate with each other will continue to reap the benefits of the cooperation. While one tribe could acquire immediate gains by betraying the other, from the moment the other tribe is betrayed they become your enemy, and while you may steal their goods and women today they will steal your possessions tomorrow and thereafter.
Because the gains of cooperating are so large, and because cooperation breaks down at the first betrayal, in this repeating game there is an equilibrium of cooperating. Year after year, the alliance continues. It might not last forever, but the forces encouraging the cooperation are generally greater than the forces inciting them to betray each other. Each side will perform acts to make the cooperate last. An Austrian princess marries a French king, binding the two nations by blood. One Yanomamo tribe holds a feast for their friends, and allows them to select one gift from their possessions to take with them as they leave. The Americans make large loans to their allies to rebuild after World War II, in case World War III is around the corner and another alliance is warranted.
Tit-for-tat
Researchers from multiple disciplines have researched various versions of this Metaphor for Society game. One example is the price-setting game, shown below, which requires two players; one pretends to be the firm ADM and the other pretends to be the firm Ajinomoto. Both firms are real firms who both sold lysine, a feed additive for livestock. If they can both charge high prices they collectively make the most money: $100 in total; $50 to each firm. If one firm believes the other will charge a high price, they can under-cut them by charging a low price, stealing their customers and making $60, which the other only makes $10. Collectively they make less, but the firm who betrayed the other made more than they would cooperating.
Study this game, and you will see that if it is played once, each firm's dominant strategy is to defect and charge a low price. When they do, they collectively make only $60, each receiving $30. When the firms are not able to coordinate with and trust each other, they do only what is best for themselves, where they engage in a price war which results in small profits for both. If they could somehow form binding agreements they would instead do what is best for both of them, and in the process each firm's profits would rise from $30 to $50.
Remember, Monsanto and Ajinomoto are real firms who engaged in this type of game, except the units in Figure 3 didn't refer to dollars, but millions of dollars, and they played the game repeatedly. As the movie The Informant illustrates, because the repetition of the game allowed them to facilitate trust, they were able to cooperate with each other and charge high prices. The cooperation made them lots money, in the short-term. You see, this type of cooperation is called collusion in the legal world, and it comes with a prison sentence and huge fines—as both firms learned!
Figure 3—Price Setting Game price setting game.jpg)
Economists have recruited random people and asked them to play this game, where each person would receive the amount given by the game in Figure 3. If each person in the experiment defected to charge a low price, each person received only $30. Some individuals pay the game only once, some play it repeatedly with different opponents in each game, and some played it repeatedly with the same person.
Computer simulations have also been conducted to determine the best combination of strategies for thriving in the game. These simulations can mimic the biological world, where individuals of a species can get along well with each and cooperate, or try to out-compete each other. The simulations show that many species should develop ways to cooperate with each other, and biological observations have proven the simulations right. The Vampire Bat in particular has maintained a lasting cooperation among its members. Each bat shares the blood it obtains on hunts with other bats couldn't find blood that night, but they only share with altruistic bats. A bat who takes blood when offerred but never shares the blood it acquires is soon shunned from the herd. Because the "jerk" bats can't find anyone to share blood with them, they compete poorly for mates and have few offspring.
This is important. The bats can only maintain their altruistic culture is they punish selfish bats, which is how they keep the genes for altruism within the herd and keep genes for selfishness out. Vampire bats, economic experiments, and computer simulations all arrive at the same conclusion that the best strategy for dealing with others is a tit-for-tat where you cooperate with people who cooperate with you, refusing to cooperate with the others. This is not only the optimal strategy but is a strategy embedded into our morality. In the price-setting game, when two people can play repeatedly, they tend to cooperate and charge high prices, knowing that the second one person charges a low price the other will do the same in the next round, leading to multiple rounds of price wars where neither make much money.
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References
(F1) Fischer, Edward. 2004. "Lecture 15: Cannibalism and Violence." Peoples and Cultures of the World. The Teaching Company.
