Gaming the Quantum

In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of "quantized games", and of applying game theory to quantum mechanics, referred to henceforth as "gaming the quantum", have become synonymous under the single ill-defined term "quantum game". Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multi-player, non-cooperative game quantum mechanical, is given. Within the context of this description, finding a Nash equilibrium in a strictly competitive quantum game is shown to be equivalent to finding a solution to a simultaneous best approximation problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.
Comment: Version 4 contains two new sections: an introduction and section 6.1. The latter section discusses how a quantum mechanism design approach can be used to contruct quantum games at Nash equilibrium. Article to appear in Quantum Information & Computation