Quantum Games

Science News, Nov 20, 1999 by Ivars Peterson

Two prisoners charged with a serious crime are held in separate cells. Their captors offer each of them the same deal.

If one testifies against the other and the other says nothing, the squealer goes free and his associate gets a heavy sentence. If both remain silent, each one gets a light sentence. If both snitch, each gets a medium sentence.

Unable to confer and lacking faith in the other's trustworthiness, each prisoner inevitably concludes that the best strategy is to spill the beans. Both end up serving a medium sentence, which is far worse than the light sentence they would have received if they had trusted each other and said nothing.

The same thing can happen when two competing stores cut prices to lure customers or when two countries are in an arms race. Even though each party makes the best possible choice from its own viewpoint, both end up worse off than if they had cooperated.

The dilemma inherent in this situation, however, can disappear in a quantum version of the game, says physicist Jens Eisert of the University of Potsdam in Germany. "The players escape the dilemma if they both resort to quantum strategies," he remarks.

Eisert, Potsdam colleague Martin Wilkens, and Maciej Lewenstein of the University of Hannover in Germany describe their approach in the Oct. 11 PHYSICAL REVIEW LETTERS.

In the standard version of the Prisoners' Dilemma, one can either squeal or stay silent. The quantum edition allows a third option: a superposition of squealing and staying silent. Moreover, the choices of the two prisoners can be entangled, so that one influences the other.

Quantum particles show just that sort of behavior. If two particles are in an en tangled state, then even if the particles are physically separated by miles, they behave in some respects as a single entity rather than two separate entities (SN: 8/5/89, p. 88).

So, when a physical process creates an entangled pair of photons of light, detecting the state of one of them automatically fixes the corresponding state of the other, even when the two photons are far apart. Quantum cryptography takes advantage of this effect (SN: 2/10/96, p. 90).

Eisert and his collaborators describe a physical model of the Prisoners' Dilemma in which both prisoners have secret access to such particles and can manipulate their states. In effect, the prisoners become quantum players.

The researchers demonstrate that the best strategy for both prisoners is initially not to squeal or stay silent. Instead, they can feel each other out using weird quantum combinations and, in the end, make the choice that rewards them.

"Very much as in quantum cryptography and computation, we have found superior performance of the quantum strategies if entanglement is present," Eisert and his coworkers assert.

At this early stage, no one knows where quantum game theory may eventually lead. Eisert, Meyer, Grover, and others have taken just the first steps into a strange, unexplored realm.

Many questions remain. Meyer, for instance, is now pondering what might happen in games that involve three or more people, when coalitions, betrayals, and shifting allegiances come into play.