Quantum game theory

Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:

Superposed initial states,

Quantum entanglement of initial states,

Superposition of strategies to be used on the initial states.

This theory is based on the physics of information much like quantum computing.

History

In 1969, John Clauser, Michael Horne, Abner Shimony, and Richard Holt (often referred to collectively as "CHSH") wrote an often-cited paper describing experiments which could be used to prove Bell's theorem. In one part of this paper, they describe a game where a player could have a better chance of winning by using quantum strategies than would be possible classically. While game theory was not explicitly mentioned in this paper, it is an early outline of how quantum entanglement could be used to alter a game.

In 1999, a professor in the math department at the University of California at San Diego named David A. Meyer first published Quantum Strategies which details a quantum version of the classical game theory game, matching pennies. In the quantum version, players are allowed access to quantum signals through the phenomenon of quantum entanglement.

In the same year, Jens Eisert, Martin Wilkens and Maciej Lewenstein published work entitled Quantum Games and Quantum Strategies that explored the role of quantum strategies in canonical two-player games such as the prisoner's dilemma.

Since Meyer's paper on the one hand and the

Eisert-Wilkens-Lewenstein paper on the other, a large number of publications have been published exploring quantum games and the way that quantum strategies could be used in games that have been commonly studied in classical game theory.