1202.4708 (Simon J. D. Phoenix et al.)

Playing Games with Quantum Mechanics    [PDF]

Simon J. D. Phoenix, Faisal Shah Khan

We present a perspective on quantum games that focuses on the physical
aspects of the quantities that are used to implement a game. If a game is to be
played, it has to be played with objects and actions that have some physical
existence. We call such games playable. By focusing on the notion of
playability for games we can more clearly see the distinction between classical
and quantum games and tackle the thorny issue of what it means to quantize a
game. The approach we take can more properly be thought of as gaming the
quantum rather than quantizing a game and we find that in this perspective we
can think of a complete quantum game, for a given set of preferences, as
representing a single family of quantum games with many different playable
versions. The versions of Quantum Prisoners Dilemma presented in the literature
can therefore be thought of specific instances of the single family of Quantum
Prisoner's Dilemma with respect to a particular measurement. The conditions for
equilibrium are given for playable quantum games both in terms of expected
outcomes and a geometric approach. We discuss how any quantum game can be
simulated with a classical game played with classical coins as far as the
strategy selections and expected outcomes are concerned.

View original: http://arxiv.org/abs/1202.4708