Definition of Troika:
Synonym of Triumvirate – An association or group of 3 ruling bodies, jointly responsible for some task.

http://gogreece.about.com/od/Glossary-of-Greek-Terms/g/The-Troika.htm

The troika is a slang term for the three organizations which have the most power over Greece's financial future - or at least that future as it is defined within the European Union. The three groups are the European Commission (EC), the International Monetary Fund (IMF), and the European Central Bank (ECB).
While Greece squeaked through the end of 2011 with the approval of the Troika for bailout packages, things got challenging during the dual elections. While many observers feel the worst of the crisis is passing, Greece's leaders are calling for additional "Greek haircuts" on existing loans and the Troika makes frequent visits to Athens...and will be until the next financial aid package is hammered out. If it is...

http://www.forexnews.com/blog/questions/who-is-the-troika/

With relation to current events, the Troika is vernacular for the 3-part commission that is charged with monitoring the Euro debt crisis. They are also responsible for making recommendations on policy to help solve the Euro debt crisis, so they wield a tremendous amount of power.

http://blogs.telegraph.co.uk/finance/ambroseevans-pritchard/100019006/who-will-hold-the-troika-to-account-for-asphyxiating-greece/

Germany has clearly taken the decision to expel Greece from the euro, whatever the new Greek government does.
Vice-Chancellor Philipp Roesler says the "horror" of Greek exit has worn off. The markets will hardly miss a beat when the day comes.
Greece has already failed to complete 210 targets imposed by the EU-IMF Troika.
"Unfortunately it is likely that Greece will not be able to fulfill the requirements. And I say quite clearly, if Greece fails to comply, there should be no more payments to Greece. I have to say I am more than skeptical," he said.
Before we all join together to kick the Greeks when they are down, let us be clear why the country has kept missing the targets.
The Troika originally said that Greece' economy would contract by 2.6pc in 2010 under the austerity regime, before recovering with growth of 1.1pc in 2011, and 2.1pc in 2012.
In fact, Greek GDP has been in an unbroken free-fall. It did not grow last year. It contracted a further 6.9pc, and is now expected to shrink 6.7pc this year.
This was entirely predictable – and was predicted by many critics – since Greece faced an IMF-style austerity package without the usual IMF cure of devaluation. The Troika's ideology of "expansionary fiscal contraction" – which the IMF has to its credit since abjured, but the fanatics in charge still swear by – is breaking a whole society on the wheel.
The result of this Great Depression – as the Greek prime minister calls it – is in implosion in tax revenues. The budget deficit has remained stuck near 9pc of GDP despite draconian wage cuts and hospital closures.
Roughly speaking, the Troika has misjudged the scale of economic decline over three years by 12pc of GDP.
"That is a massive miscalculation," said David Bloom, head of currencies at HSBC.
"The collapse has been exponential. Greek GDP is contracting faster than they can reduce debt. The Troika really has a duty to give Greece the next tranche of money," he said.
As for the failure to carry out the privatisation programme (mostly property), how on earth is Greece supposed to comply? Mass sales of real estate right now would tip the property market into an even deeper downward spiral, taking the economy with it.
It is a lonely task sticking up for the Greeks – given the sins of their elites over the last decade – but do we really have to put up with the false narrative coming from the EU's creditor core, and the self-serving eyewash by the policy architects of this disaster in Brussels, Frankfurt, and indeed Washington?
What Mr Roesler really means is that Germany is not willing to spend any