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Everyone wins in quantum games

The best way to win a game like 'paper-stone-scissors' is to use "quantum rules". Baffle your opponent by pulling out a hand that is simultaneously 'paper' and 'scissors', says Phil Ball.

Quantum mechanics got Schrödinger's cat into a sticky situation, but it can rescue you from dilemmas too. Three physicists working in Germany claim in the journal Physical Review Letters1(11 October issue) that a game that typically ends in a kind of frustrating stalemate ceases to do so if played with "quantum rules".

The game is called the Prisoner's Dilemma, and it pitches two players against one another in a manner reminiscent of the playground game of paper-scissors-stone. The players can choose to 'cooperate' or 'defect', and receive a certain payoff depending on their choice and their opponents. The 'dilemma' is that the payoffs imply that a rational player should always defect; yet they both get a better payoff for mutual cooperation than for mutual defection.

This game serves as a model for individuals selecting strategies in competitive scenarios both in evolution and human social and political systems. It appears to suggest that cooperation can arise only if we can overcome our 'rational' instinct towards selfishness. But now Jens Eisert and Matrin Wilkens at the University of Potsdam, along with Maciej Lewenstein at the University of Hannover, have shown that there is a Third Way: to play using quantum strategies. This, they say, creates a new best strategy that offers the reward only the irrational, cooperative strategy secures in our 'classical' world.

How do you play a game with quantum rules? In the classical Prisoner's Dilemma, one can make only a single choice: cooperate or defect. The curious thing about quantum systems, however, is that they can exist neither in one state nor another, but in a mixture - a superposition - of both, like Schrödinger's hypothetical cat, which was simultaneously dead and alive.

In the paper-scissors-stone game, this would be analogous to whipping out a hand that is both paper and scissors at the same time - not half of each, or halfway between the two, but capable of "collapsing" into either pure state.

But the quantum game can be even more strange, because it is possible in this case to make the choices of the two players "entangled", so that each influences the other. When two quantum particles, such as photons of light, are created in an entangled state, making a measurement on one of them automatically fixes the corresponding property of the other.

In an entangled game, the researchers show that the best strategy of both players is neither to defect nor to cooperate, but to offer some strange concatenation of the possible outcomes open to them. It is hard to give any classical description of this strategy, other than to say that when both players use it, they both come off as well as they possibly can. In other words, this quantum strategy is not only the most rational but also the most profitable. There is no longer any dilemma.

Of course, real creatures play the game in a classical world, where defection or co-operation are the only options. But Eisert and colleagues point out that some aspects of their quantum game resemble the interactions that go on when information is exchanged quantum-mechanically - something that has been shown to ensure secure communication of coded signals. Perhaps the greatest significance is philosophical, however: quantum mechanics can dissolve deadlocks that, according to classical logic, appear insuperable.


  1. Eisert,J., Wilkens, M., & Lewenstein, M. Quantum Games and Quantum Strategies Physical Review Letters 83, 3077 - 3080 1999.

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Ball, P. Everyone wins in quantum games. Nature (1999).

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