Macroeconomics For Dummies®, uk edition Published by: John Wiley & Sons, Ltd

Finishing the game

To ‘solve’ (work out the likely outcome of) the game, you need to use a procedure called backward induction. This process involves going to the end of the game, working out what players will do if they’re called upon to act and then working backward until you reach the start of the game.

Here, the government acts last: it has to decide what to do if the banks take on excessive risk. Looking at the payoffs to the government, it has to choose between –1,000 and –50. Clearly –50 isn’t great, but it’s a lot better than – 1,000. Thus, you can be quite confident that if the government is faced with a choice between bailing out and not bailing out, it will choose to bail out.

Moving back to the start of the game, the banks have to decide between moderate and excessive risk. They already know (because they understand backward induction) that if they take excessive risk, the government will

choose to bail them out. Thus, the banks face a choice between a payoff of 10 (if they take moderate risk) and 50 (if they take excessive risk, safe in the knowledge that a bailout will be forthcoming).

Therefore the outcome of the game is that banks take on excessive risk and the government bails them out. Economists call this the subgame perfect equilibrium of the game, because it was derived using backward induction: that is, when deciding how to act, the banks looked into the future and thought about how the government was likely to act if they took on excessive risk (see Figure 15-5).

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Figure 15-5: Subgame perfect equilibrium.

Notice that if the government had announced at the start of the game that it wouldn’t bail out banks if they took excessive risk, and banks

believed the threat, the banks would prefer to take moderate risk (a payoff of 10) rather than excessive risk (a payoff of –100). Economists call these kinds of threats incredible threats, because when push comes to shove they won’t be carried out. For this reason, rational decision-makers should rule out incredible threats, which is precisely what performing backward induction does.


In the example, the banks should consider Obama and Cameron’s statement that they won’t bail out banks to be an incredible threat, because in a time of crisis they’ll have no incentive to stick to their statement and every incentive to bail out the banks!