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Modelling risk-taking as a Prisoner’s Dilemma
When a bank decides to take on excessive risk, it not only increases the chances of getting into financial difficulties, but also increases the chances that other banks will too. This is because of the highly interconnected nature of the financial system (see Chapter 14).
Here we show how the incentives that banks face can be thought of as a ‘Prisoner’s Dilemma’ – where each bank finds it in its interest to take excessive risk even though this leads to a highly unstable financial system and increases the probability that it will fail.
Affecting others negatively
Economists say that one bank deciding to take on excessive risk has a negative externality on all the other banks, because it makes the entire financial system less stable. An externality is a positive or negative effect on a third party. For example, if someone lights up a cigarette and smokes it standing right next to you, as well as being very rude that person is also causing a negative externality. In contrast, if you choose to get your child immunised from all sorts of nasty illnesses, you’re reducing the chances of other children getting ill as well – this is an example of a positive externality.
Economists are interested in activities that create externalities, because if left to their own devices, people undertake too much of an activity that creates negative externalities and too little of an activity that creates positive externalities.
Seeing the Prisoner’s Dilemma
Left to their own devices, banks don’t take into account that their risk-taking activities have a negative impact on other financial institutions. For this reason they all tend to want to take on too much risk. The resulting outcome (all banks taking on excessive risk) leads to an exceptionally unstable financial system. Ironically, all the banks would be better off if they all took only moderate risks, because this would ensure the stability of the financial system. Economists call these types of scenario the Prisoner’s Dilemma.
Imagine that you and a friend carry out a robbery (not that For Dummies readers ever would, but just play along). You’re not particularly skilled robbers and the police quickly catch you. They know that you’re the culprits, but they lack enough evidence to charge you. They do, however, have sufficient evidence to charge you for a less serious crime (say, trespass).
The only way they can put you away for robbery is if one of you confesses to it. Clearly, confessing to your crime doesn’t seem like a wise move: you’ll both go to jail for many more years than if you just keep quiet.
Here’s the twist. A particularly cunning police officer separates you and your friend so you can’t communicate and offers you the following deal: if you confess to the crime and your friend doesn’t, you get off scot-free but your friend does 15 years. If you both confess, you both go to jail for ten years, and if you both deny, you both go to jail for one year for trespassing. The same offer is made to your friend. Assuming that your only objective is to minimise the amount of time that you spend in jail, what should you do?
To try to answer these kinds of questions – where you have to think strategically – economists model them as games (in the sense of any situation where the outcome depends not only on your own actions but also on the actions of others). Figure 15-1 models the Prisoner’s Dilemma as a normal form game.
© John Wiley & Sons
Figure 15-1: The Prisoner’s Dilemma.
A normal form game has to specify three things:
Players: The Prisoner’s Dilemma has two players, you and your friend.
Possible actions each player can take: Here each player has to decide whether to ‘Confess’ or ‘Deny’.
Payoffs: How good (or bad) each outcome is for the different players.
Looking at Figure 15-1 you can see the four possible outcomes. Associated with each outcome are the payoffs, in this case how long you and your friend go to jail (the minus signs show that you dislike going to jail): the first number is your payoff and the second number is your friend’s. For example, if you deny and your friend confesses, you get a payoff of –15 and she gets a payoff of 0.
The important thing to notice is that regardless of what your friend does, you’re better off confessing. You can check this for yourself:
Your friend denies: You can either deny (in which case you go to jail for a year) or you can confess (in which case you don’t go to jail).
Your friend confesses: You can either deny (in which case you go to jail for 15 years) or you can confess (in which case you go to jail for 10
years).
Therefore, confessing is your dominant strategy, because it’s better than any other course of action available to you, regardless of what your friend does. Notice that confessing is also a dominant strategy for your friend (spend a moment looking at Figure 15-1 to convince yourself). Even though you’ve both done what’s best for yourself, the resulting outcome where you both confess looks quite bad – you both go to jail for ten years. Had you both kept quiet you’d only have spent a year in prison each. You have a dilemma; more precisely, you have a Prisoner’s Dilemma!
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