Analysts said on Wednesday that having Greece buy back its own devalued bonds could be an important step toward solving Europe’s sovereign debt crisis.
It's an interesting equilibrium. Let's say Greek bonds are selling for 60 cents on the dollar. If the Greek government offers sixty-one cents, arguably the government is signaling a more optimistic prognosis than a 60 cent value or even a 61 cent value for the bond. Don't sell ("beware of Greeks bearing gifts!"). If everyone is a rational Bayesian, the price of bonds should go up to the point where the Greek government doesn't want to buy the bonds any more or where indifference holds.
If buying back some of the bonds makes the rest of the debt easier to pay back, all the more reason not to sell your bonds at the initial offer price.
The purchase might work if the Greek government can signal they don't have inside information about their own ability or willingness to pay back the money. That's hard to do, but not impossible. After all, companies do buy back their own shares and I don't think tax arbitrage is the only motive. For instance the company also may wish to shift the composition of its creditors and perhaps governments have the same motive. Then the purchase can be a win-win.
Another equilibrium is if the Greek government offers to buy back the bonds with some probability. Sellers might then play a mixed strategy in response and maybe then we are getting somewhere, with some probability that is. These games usually are complicated and if you don't already get the intuition here don't bother with it.
Overall, the schemes are unlikely to work in practice.