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(A.1) Prisoners' Dilemma
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 in strategic interactions, where the outcome of a player's strategy depends on the strategies chosen by others, such as the case of most card and board games, they are participating in a field of economics called game theory.
Figure 1—Prisoners' Dilemma
prisoner dilemma better.jpg)
(A.2) Game Theory: Dominant Strategy Equilibrium
It is easy to develop a logical prediction of what each prisoner will decide in the Prisoners's Dilemma. 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.
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 their actions do not change your optimal strategy. 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 we predict that both players will 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.
(B.1) 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 each other about it. Ideally they would have a serious conversation and then sign some sort of enforceable contract requiring neither party to confess. That is not the setting of the game, though. In fact, the police designed it to prevent the prisoners from colluding with each other.
So if each prisoner pursues only 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 discourage us from doing so. 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 an undesirable 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.
(C.1) 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? The prisoners only play the game once, but we interact with the same people over and over throughout our lives, and if we only act 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 (forgive my language, but it seemed necessary), and no one will want to work with us, do us a favor, or even consider working together. They might even go out of their way to hurt us in revenge for what we did to them. What we are playing is something like the Prisoners' Dilemma game, except that it is played repeatedly, and between the same two prisoners. I call this repeating Prisoners' Dilemma game a Metaphor for Society.
When the Prisoner's Dilemma is repeated over and over, the moment you betray the other person they will likely betray you in the future. You both now find yourself stuck in a spiral of hatred, neither of you able to enjoy the benefits of human cooperation. Every iteration you both earn -2, when if both cooperated you both gain + in each round. Every iteration, you lose, when you could be gaining, all because you cared only about your immediate self-interest and not your long-term well-being.
Figure 2—Metaphor for Society
 metaphor for life.jpg)
(C.2) Tit-for-tat, with possible forgiveness
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, whereas the other only makes $10. Collectively they make less, but the firm who betrayed the other made more than they would make 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 both defect 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.
Figure 3—Price Setting Game
 price setting game.jpg)
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!
The government makes collusion illegal because it knows that when firms routinely compete with each other they have the incentive to cooperate and charge high prices, which would be bad for consumers. The government is more concerned with protecting consumers from high prices than they are the freedom of businesses.
Video 1—The Informant, a Movie About Collusion in the Lysine Market
Economists have recruited random people and asked them to play this price-setting 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 play the game only once, some play it repeatedly with different opponents in each game, and some play it repeatedly with the same person. How people behave in these experiments provides a wealth of information about the psychology of human cooperation. What they find is that humans are hard-wired for cooperation, and if people play the ga,e repeatedly against the same person, they quickly learn to cooperate and charge high prices
Computer simulations have also been conducted to determine the best combination of strategies for playingin the game. These simulations can mimic the biological world, where individuals of a species can get along well with each other 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 that couldn't find blood that night, but they only share with altruistic bats. A bat who takes blood when offered 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 consume less nutrients, compete poorly for mates, and have few offspring. Consequently, if the altruistic have the most offspring, their altruistic genes proliferate, and the species as a whole displays altruism.
What experiments and simulations show is that people tend to behave in a tit-for-tat fashion, with possible forgiveness. When others are nice to us we repay them with kindness. When others harm us we seek to harm them also. However, we do periodically forgive others, if we think they will repay us by becoming kind, but forgiveness is never guaranteed. As a result, when given enough time, players almost always learn to cooperate. The prisoners learn to never confess in the [repeating] Prisoner's Dilemma game,and the firms always charge high prices in the [repeating] price-setting game.
In short, people learn to be nice to others, not for the sake of the other person, but in regards to long-run self-interest.
When it comes to our interactions with others, we engage in reciprocity, with periodic forgiveness. That is our human nature, and it is also the optimal strategy in the repeating Prisoner's Dilemma.
(C.3) The potash cartel dissolves into "every man for himself"
U.S. Antitrust laws are only effective in the U.S., but most potash (the main ingredient used to make potassium fertilizer) is obtained from a few international mines. This has made collusion among the potash producers relatively easy to execute, and that is indeed what has happened in the past. Most potash has been sold through only two marketing groups, who have tended to set identical prices in India and China.
In August of 2013, one Russian potash producer (producing one-fifth of all potash) elected to renege on this collusion and go at it alone. The producer, Uralkali, can produce at a lower cost than its former partners, so it decided it could make more money by competing against other potash producers than colluding with them. This serves as an important lesson: collusion tends to occur among equals.
The price of potash is naturally expected to fall. The Economist magazine expects it to fall 25%. As prices fall more potash will be purchased, more fertilizer applied, and more food produced.
Video 2—The Potash Collusion Ends
(D) Tit-for-tat and markets
This insight into the prevalence of tit-for-tat or reciprocity is profound. Much of our morality is driven by notions of reciprocity—regardless of whether it is taught in a religious setting—because only in settings of reciprocity will humans willingly cooperate with one another and thrive.
Most of our wealth comes from trade with strangers. After all, you don't know hardly anyone who made the goods you consume. You earn money and buy the goods in a market, and if you think about it, markets are just a series of reciprocating interactions. I give Wal-Mart $50, and it gives me $50 worth of stuff.
Trade with strangers—at its core—emanates from a natural morality of reciprocity.
