Greece is much closer to Nash’s complicated scenarios, said Barry Nalebuff of the Yale School of Management, a game theory expert. “Both sides agree it’s better not to push Greece over the cliff. But how far can you push? Each side knows the other side should be willing to make concessions because it’s in their interest. Neither side does because they believe the other side will. So there’s a standoff. It’s very hard when it’s in both side’s interests and there are multiple solutions or equilibria, which is the situation with Greece.”

Mr. Varoufakis agreed that in the Greece example, “the game has multiple equilibriums and, therefore, a failure to agree may trigger a chain of outcomes that no one can either predict or control.” He added, “We have many interlocutors. Some are painfully aware of the disaster that awaits Europe if Greece defaults. Others are less aware. Some are utterly unaware. They think it can be contained. There’s a great divergence of opinion on the other side regarding the potential outcome. Even in Germany, there are many divergent views.”

Uncertainty of outcome vastly complicates any game theory analysis. Citing the work of the University of Chicago professor Frank Knight, Mr. Varoufakis pointed to the difference between risk and uncertainty. Betting on the flip of a coin involves high risk, but the potential outcomes and probability are known. “Uncertainty is when you can’t know all the outcomes or the probability with which each potential outcome will occur,” he said. “This is deep uncertainty.” Complicating matters further, “these negotiations are also about hearts and minds, both of the participants and of the wider community — investors, citizens in Greece and outside of Greece. Those who think that game theory can cut through this Gordian knot are badly mistaken.”

Kenneth Rogoff, the Harvard economist and expert in financial crises, agreed the uncertainty of outcomes should Greece default has contributed to the continuing impasse. “Would a Greek default be contained? Would it trigger another global financial crisis? Greece is in a tough situation regardless,” he said. The Germans might underestimate the risk of contagion from a Greek default, as the United States government underestimated the consequences of a Lehman Brothers failure. “It’s a mess,” Mr. Rogoff concluded. “If you’re in a game where we don’t know what will happen, game theory has little predictive power.”

No one I spoke to this week thinks the situation is hopeless. Mr. Nalebuff said that one of Dr. Nash’s most important contributions is the notion of allocentrism, which requires parties to assess the others’ interests in order to understand their bargaining position. (It’s the opposite of egocentrism.) In order to know how far they can push Greece, its creditors need to “understand the interests and objectives of the Greek government. And Greece needs to come up with a solution that works for Germany,” Mr. Nalebuff said. “This could be very constructive,” although it’s no guarantee that an optimal solution will be reached.