Prisoner's Dilemma
Game theory is the study of the types of interractions, and the prisoner's dilemma is one of the most common and useful type of game.
The standard story goes like this: Two criminals are caught and charged with robbing a bank. The prosecutor has enough evidence to convict them for minor crimes, but unless she can get them to confess, she can't convict them for the robbery. Each prisoner can go free if they testify against the other prisoner and blame them, but if they both confess, they will both go to jail for 5 years. If the prosecutor gets one of the criminals to confess, that criminal will blame their partner for everything, leading to a harsh sentence.
If B is silent, A will want to confess, because going free is better than a year in prison.
If B confesses, A will want to confess, because 5 years imprisonment is better than 10 years.
No matter what B does, A will want to confess, and vice versa.
Each prisoner seeking their own self interest will lead to a worse situation for both of them. Both prisoners would prefer 1 year to 5 in prison, yet they will always have an incentive to confess. Cooperation can lead to better outcomes than self interested actions.
There are many variations on the prisoner's dilemma. Every variation results in slightly different outcomes so it is important to keep in mind the peculiarities of each individual situation when describing it in game theoretic language. Are the players allowed to communicate? People who can talk can discuss what they will go and increase their chances of cooperating. How many players are there? The more participants there are, the harder it is to communicate, but the higher the gains from communicating. Depending on how much there is to gain, it might be worth forming a coalition of cooperators, even if there are some defectors. Is there an outside agent that can enforce contracts, or make rules to help the players cooperate? For example, the government could pass a law forcing people to cooperate. Are there property rights that can be defined that can increase the odds of cooperation? According to the Coase theorem, if transactions costs and income effects are small, people can solve All these questions must be answered to address real life prisoner's dilemma situations. The best way to learn how to think about prisoner's dilemmas is to look at examples.
Prisoner's Dilemma situations can occur because of negative externalities. An action that helps one person but hurts others in the community will tend to be done more than is efficient. The overuse is often called the Tragedy of the Commons. Imagine you have a field where herders graze their sheep. If they all leave their sheep on for a long time, the grass dies and they get thin sheep. If one farmer leaves their sheep on for a short time and the other farmer leaves them on for a long time, the farmer who leaves them on for a long time gets fat sheep. If they both limit themselves, they can both have healthy sheep. Fisheries also exhibit this property. If all fishermen fish as much as they like, the fish stock gets depleted. Most fishermen need to exhibit self control to preserve fish stocks.
Prisoner's Dilemma situations can also occur with positive externalities - when the benefits of an action are not gained fully by the people doing it. Lighthouses are the standard example of a good that may not be produced enough because of coordination problems. It is hard to provide one boat with a lighthouse without providing all boats with a lighthouse. There is also the hold-up problem where a lighthouse owner could turn off the lighthouse until a boat paid a large fee lest it turn back or be destroyed on the rocks. However, lighthouse owners solved this problem by bundling the fee for a lighthouse in with other goods, such as docking fees. Since science benefits all mankind, it tends to be under produced. A single person may want to free ride on the inventions and discoveries of others. Since the total stock of knowledge does not depend on any single scientist, they have little incentive to solve the problem themselves. Fortunately, society has evolved many ways to solve this problem, and human beings are status seeking, so we like to get respect from others, even if we don't get money. Another way to say it is that we can get respect by being rich, but we can also get status by showing off how smart we are by solving complicated scientific problems.
Another source of prisoner's dilemma situations is when relative levels matter more than absolute levels. For example, during the Cold War, the U.S. and Soviet Union did not care how many nukes they had, as long as it was more than the other side. Peacocks don't care how nice their tails look, as long as they are nicer than their rivals. It is more important to an elephant seal that it is bigger than its rivals, even though it is easier to survive at a lower weight. Thomas Schelling noted that when players vote on hockey masks, they are typically highly in favor of them, however, when they are optional, few players wear them. Not wearing a mask gives a player a competitive advantage over those that do, but if everyone doesn't wear one, no one gets and advantage and everyone suffers the higher risk of injury. Dumping resources into an arms race raises the absolute level of performance but makes no one person better off relatively.
Prisoner's dilemmas are almost always framed as a bad thing, but that does not have to be the case and indeed they can be arranged to work to improve society. Economic competition is a primary example of a prisoner's dilemma that helps people overall. All producers want to raise their prices to get higher profit, but if one producer raises their price, and the other does not, the lower price competitor will get all the business and make more money. If they both lower their prices, neither of the producers benefit, but the customers are much better off. Product innovation is an arms race. As producers expend resources improving their products, they gain a temporary boost in market share and profit, but as their competitors race to catch up and release their better products, the advantage is competed away. Each producer would like to make an agreement with the other producers to keep prices high and innovation low, but because of the prisoner's dilemma, they are forced to do neither. Prisoner's dilemmas are found throughout society, for better and for worse and solving them (when they are bad) can be one of the most difficult problems a society can face.
The standard story goes like this: Two criminals are caught and charged with robbing a bank. The prosecutor has enough evidence to convict them for minor crimes, but unless she can get them to confess, she can't convict them for the robbery. Each prisoner can go free if they testify against the other prisoner and blame them, but if they both confess, they will both go to jail for 5 years. If the prosecutor gets one of the criminals to confess, that criminal will blame their partner for everything, leading to a harsh sentence.
If B is silent, A will want to confess, because going free is better than a year in prison.
If B confesses, A will want to confess, because 5 years imprisonment is better than 10 years.
No matter what B does, A will want to confess, and vice versa.
Each prisoner seeking their own self interest will lead to a worse situation for both of them. Both prisoners would prefer 1 year to 5 in prison, yet they will always have an incentive to confess. Cooperation can lead to better outcomes than self interested actions.
There are many variations on the prisoner's dilemma. Every variation results in slightly different outcomes so it is important to keep in mind the peculiarities of each individual situation when describing it in game theoretic language. Are the players allowed to communicate? People who can talk can discuss what they will go and increase their chances of cooperating. How many players are there? The more participants there are, the harder it is to communicate, but the higher the gains from communicating. Depending on how much there is to gain, it might be worth forming a coalition of cooperators, even if there are some defectors. Is there an outside agent that can enforce contracts, or make rules to help the players cooperate? For example, the government could pass a law forcing people to cooperate. Are there property rights that can be defined that can increase the odds of cooperation? According to the Coase theorem, if transactions costs and income effects are small, people can solve All these questions must be answered to address real life prisoner's dilemma situations. The best way to learn how to think about prisoner's dilemmas is to look at examples.
Prisoner's Dilemma situations can occur because of negative externalities. An action that helps one person but hurts others in the community will tend to be done more than is efficient. The overuse is often called the Tragedy of the Commons. Imagine you have a field where herders graze their sheep. If they all leave their sheep on for a long time, the grass dies and they get thin sheep. If one farmer leaves their sheep on for a short time and the other farmer leaves them on for a long time, the farmer who leaves them on for a long time gets fat sheep. If they both limit themselves, they can both have healthy sheep. Fisheries also exhibit this property. If all fishermen fish as much as they like, the fish stock gets depleted. Most fishermen need to exhibit self control to preserve fish stocks.
Prisoner's Dilemma situations can also occur with positive externalities - when the benefits of an action are not gained fully by the people doing it. Lighthouses are the standard example of a good that may not be produced enough because of coordination problems. It is hard to provide one boat with a lighthouse without providing all boats with a lighthouse. There is also the hold-up problem where a lighthouse owner could turn off the lighthouse until a boat paid a large fee lest it turn back or be destroyed on the rocks. However, lighthouse owners solved this problem by bundling the fee for a lighthouse in with other goods, such as docking fees. Since science benefits all mankind, it tends to be under produced. A single person may want to free ride on the inventions and discoveries of others. Since the total stock of knowledge does not depend on any single scientist, they have little incentive to solve the problem themselves. Fortunately, society has evolved many ways to solve this problem, and human beings are status seeking, so we like to get respect from others, even if we don't get money. Another way to say it is that we can get respect by being rich, but we can also get status by showing off how smart we are by solving complicated scientific problems.
Another source of prisoner's dilemma situations is when relative levels matter more than absolute levels. For example, during the Cold War, the U.S. and Soviet Union did not care how many nukes they had, as long as it was more than the other side. Peacocks don't care how nice their tails look, as long as they are nicer than their rivals. It is more important to an elephant seal that it is bigger than its rivals, even though it is easier to survive at a lower weight. Thomas Schelling noted that when players vote on hockey masks, they are typically highly in favor of them, however, when they are optional, few players wear them. Not wearing a mask gives a player a competitive advantage over those that do, but if everyone doesn't wear one, no one gets and advantage and everyone suffers the higher risk of injury. Dumping resources into an arms race raises the absolute level of performance but makes no one person better off relatively.
Prisoner's dilemmas are almost always framed as a bad thing, but that does not have to be the case and indeed they can be arranged to work to improve society. Economic competition is a primary example of a prisoner's dilemma that helps people overall. All producers want to raise their prices to get higher profit, but if one producer raises their price, and the other does not, the lower price competitor will get all the business and make more money. If they both lower their prices, neither of the producers benefit, but the customers are much better off. Product innovation is an arms race. As producers expend resources improving their products, they gain a temporary boost in market share and profit, but as their competitors race to catch up and release their better products, the advantage is competed away. Each producer would like to make an agreement with the other producers to keep prices high and innovation low, but because of the prisoner's dilemma, they are forced to do neither. Prisoner's dilemmas are found throughout society, for better and for worse and solving them (when they are bad) can be one of the most difficult problems a society can face.