Crawl Across the Ocean

Wednesday, March 18, 2009

3. The Prisoner's Dilemma

links to Part 1 and Part 2

The last post in this series talked about externalities and before moving along from that topic I want to highlight two particular types of externalities.

In this post, I want to talk about the situation where two (or more) people enter into transactions with other parties that have negative externalities that affect each other - negative externalities that are large enough to wipe out any gain they made from their initial transaction.

An example will make this clearer, and we might as well start with the example that gives this particular type of situation it's name, the Prisoner's Dilemma.

Wikipedia summarizes the classic 'Prisoner’s Dilemma' situation as follows:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

Let's call one prisoner Larry and the other Curly. Put yourself in Larry’s shoes. If Curly is going to stay silent to protect Larry, Larry would be better off to betray him (and go free). If Curly is going to betray Larry, Larry is still better off to betray him and take the 5 year sentence rather than the 10 year sentence. The same logic holds true for Curly.

So Larry makes a win-win transaction with the detective (to betray Curly) but this transaction has a negative effect (externality) on Curly. Similarly, Curly makes a win-win transaction with the detective that has a negative effect on Larry.

To summarize:

Transaction 1, Larry makes a deal with the detective: Detective +, Larry +, Curly --
Transaction 2, Curly makes a deal with the detective: Detective +. Larry --, Curly +
Net Result: Detective ++, Larry -, Curly -

Now, you might argue that if Larry thinks Curly is going to stay silent to protect him, then Larry is not better off to turn Curly in, because Larry owes Curly the same sort of protection, or that Curly will remember that Larry turned him in and take revenge once he gets out of jail or because Larry will feel bad about turning Curly in. All of those things may be true, but if they are, that doesn't mean that this is a case where the prisoner's dilemma can be 'overcome' it just means that a true measure of the costs and benefits of each action needs to incorporate more factors than just the length of the prison sentence.

But, as long as we are in a situation where Larry’s payout (including the number of years of jail time, his own sense of ethics, concerns about retribution from Curly, etc.) is higher ratting on Curly vs. reciprocating Curly’s loyalty, then the situation is a prisoner’s dilemma and Larry will rat on Curly. The situation where some other factors at work lead Larry and Curly to stick together and not cooperate with the police is some other situation, not a Prisoner's dilemma.

In other words, the point is not how do we get someone to cooperate in a prisoners dilemma, the point is how can we change the payouts such that the situation is no longer a prisoners dilemma. For example, an organized crime family uses a 'law of silence' to introduce a moral code of loyalty which shifts the incentives for the prisoner's to rat each other out. On top of that, a credible threat to kill anyone who talks to the police shifts the relative payouts even further.

The result of the prisoner’s dilemma is that, for the people in the dilemma, they take an action designed to further their interests, but the end result does not end up serving their interests as they expected. Larry and Curly will both end up serving 5 years in jail when they could have just served two if they had only cooperated (with each other, not the police).

It is important to realize that the Prisoner's Dilemma is not just some contrived situation that hardly ever occurs in the real world, it is in fact almost ubiquitous in our lives. In the human world any time a party has something valuable to 2 or more other parties and plays them off against each other (e.g. an auction where people have to bid against one another, a customer that negotiates a lower price based on what a competitor is offering, etc.) you have a potential prisoner's dilemma.

In the natural world, any time two or more parties are sharing a common resource you have a potential prisoner's dilemma (e.g. tragedy of the commons)

Note that in the case of the two prisoners, they were reacting not to each other but to the offer made to them. There was no sense that first Larry would make a decision and then Curly would make a decision in response to Larry's decision. But the Prisoner's Dilemma can arise in that sort of reactive situation as well, only here you tend to get into 'Arms Race' type situations.

For example, I decide to tear down my modest house and build a monster home because I have a desire to have the largest house on the street. This is a win for me because it increases my satisfaction to come home and pull in to the largest house on the block. But it is a negative for my neighbour who now feels inferior - so he tears down his house and builds a bigger house on his lot. A win for him, but a negative for me. So I tear down my monster home and build an even bigger home. Each transaction is voluntary and is rational in the sense that it benefits the people making the transaction, but again the net result is that people are worse off because the zero sum nature of their goal (only one person can have the biggest house on the block) means that the negative externalities from each transaction outweigh the benefits.

Another more realistic example is when a Province decides it can lure away business from other Provinces by offering a lower corporate tax rate. This benefits that Province, until other Provinces retaliate by lowering their tax rates. Given the time lags, you can always point to how one Province is benefitting from lowering their corporate tax rates (for a while) but in the end, they all just end up collecting fewer taxes and there is no net benefit since there can always only be one jurisdiction with the lowest tax rate.

So the prisoners dilemma represents a special case of externalities in which the parties simultaneously or sequentially impose negative externalities upon each other such that even though every transaction is a win-win for the parties involved (Larry’s deal with the police is a win-win, and so is Curly’s deal with the police) the negative externalities mean that the parties stuck in the dilemma end up worse off.

The Prisoner's Dilemma is central to the points I eventually want to get to (I think) but there's too much material to cover in just one post, so I'll definitely be coming back to it in later posts. There's just one other point worth mentioning in this introduction and that is to note how the Prisoner's Dilemma gets harder to deal with as the number of parties involved escalates.

There are two dynamics at work here. One is that with a large number of parties, even an action that has a small negative externality per person affected can be a net negative. Take, for example, littering - the impact of litter on any given person is small, but since it affects many people the overall result is negative. The second element is that with a large number of people it is harder to change/structure the incentives so that the situation is no longer a prisoner's dilemma. With just two prisoner's, maybe Larry and Curly have a strong enough bond of loyalty to not rat each other out, but with a dozen prisoner's, somebody is likely going to talk.

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