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Can game theory explain the Greek debt crisis?

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The Greek finance minister is an expert in game theory. Could this help predict how the Eurozone negotiations will turn out, asks Marcus Miller, professor of economics at the University of Warwick.

Game theory is what its name implies. It's the use of games to study behaviour and decision-making.

The most famous game of all is the Prisoner's Dilemma. Imagine two prisoners have to choose between confessing and staying silent. If they both stay silent, they both go to jail for one year. If one confesses and the other stays silent, the first goes free and the second gets 20 years. If both confess, they both get five years.

Neither can communicate with the other. So, rationally, what should each do? Sadly for the prisoners - but not the jailer - the answer is for both to confess.

Now, take the situation facing the Greek government, which needs a deal with its eurozone partners within days to secure to avoid defaulting on its debts. Will it have the same unfortunate outcome as the Prisoners' Dilemma?

Yanis Varoufakis, the Greek finance minister, spent his academic career (which included teaching posts at the University of Essex and the University of East Anglia) studying game theory.

In February 2015, he denied that he was "busily devising bluffs, stratagems and outside options" using game theory to "improve upon a weak hand".

Nevertheless, game theory should apply in situations like this where the outcomes for each player depend on the actions of both. The world being an uncertain place, random chance may also play a role - game theory takes account of this, too.

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image captionThe Greek finance minister Yanis Varoufakis is an expert on game theory

So how might Varoufakis have visualised negotiations with the rest of the eurozone panning out?

He may well have drawn a decision-tree like that shown below, with Greece and the eurozone partners as key players. He would also include random outside factors, referred to in game theory jargon as "nature", which may also affect the outcome.

The outcomes, known as payoffs, of each player when the game ends are shown in brackets - so (1, 0) would be a good payoff for Greece and a bad one for the eurozone, whereas (1,1) would be good for both and (0,0) would be bad for everyone.

So what does the decision tree imply?

Imagine Greece moves first to avoid default by putting a plan on the table. This plan involves new taxes on the wealthy and changes to pensions - avoiding spending cuts and and having some of its debts written off in exchange. If this plan is accepted by the rest of the eurozone, then Greece is content. Let's give its payoff a score of 1.

To work out how the rest of the eurozone will respond, one has to see what they stand to gain by accepting Greece's plan, or by rejecting it.

If the eurozone accepted this deal, the monetary union would remain intact, but it would have to ease its strict rules on fiscal policy and take a loss on holdings of Greek debt. Let's give the eurozone payoff a score of ¾. So the overall payoff is (1, ¾ ).

What if the eurozone rejected the deal? Then Greece, unable to pay its creditors on time, would be in what is called "technical default".

What follows next is not at all clear. Let's look at two possibilities.

First there could be "Grexit" - Greece alone leaves the eurozone but the other members live happily ever after.

Second, Greek departure leads to the collapse of the eurozone.

The first scenario is likely to be pretty bad for Greece but not for the eurozone - a payoff of (0,1). The second is bad for everyone - the payoff is (0,0).

The truth, of course, is that no one really knows which of these will transpire - here is where nature throws the dice. If the two prospects are equally likely, the expected payoffs look pretty bad for both players.

So what is the bottom line? Faced with the messy prospect of letting Greece slide into default - and the significant risks of chaos that this entails - it looks better for eurozone partners to avert default and accept the Greek plan - or a watered-down version of it - after all.

This is better for Greece too - so unlike the Prisoner's Dilemma both players avoid the bad stuff.

This may be what has been concluded - if so, there will be a settlement with no technical default at the end of the month. But a lot depends on how well the agreed plan works. If it is a botched job, the drama may be repeated. Such is the game of life.

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Game theory can be described as the mathematical study of decision-making, of conflict and strategy in social situations. It helps explain how we interact in key decision-making processes.

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