Yanis Varoufakis is Greece’s finance minister and a master at Game Theory. He worked out expected payoffs for the two players (Greece, European Union) and created a decision tree.
Judging by the decision tree the obvious decision for Greece is to avoid defaulting and submit a three-point financial plan to the Eurozone. If the plan is accepted, Greece would be happy and the EU “would have to ease its strict rules on fiscal policy and take a loss on holdings” which is why they have a payoff of 3/4.
If the EU ends up rejecting the deal then outside factors come into play. Then one of two options could happen: Greece could exit and leave the rest of the Eurozone unaffected, or the entire Eurozone would collapse and everyone loses. Since either one has a relatively equal chance of happening the payoffs are split.
So conclusively, the mixed strategy equilibrium would be for Greece to offer the plan and the European Union to accept it. Whether the EU is willing to take the risk of rejecting the plan and avoiding the collapse of the Eurozone instead of negotiating Greece’s plans is up to them. And as the article puts “Such is the game of life”.