Physics – Quantum Physics
Scientific paper
2007-02-16
Journal of Physics A: Mathematical and Theoretical 41 (2008) 135303 (29p).
Physics
Quantum Physics
40 pages, 9 figures, PlainTeX
Scientific paper
10.1088/1751-8113/41/13/135303
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric games and obtain a complete set of quantum Nash equilibria. Apart from those available with the maximal entanglement, these quantum Nash equilibria are extensions of the Nash equilibria in classical game theory. The phase structure of the equilibria is determined for all values of entanglement, and thereby the possibility of resolving the dilemmas by entanglement in the game of Chicken, the Battle of the Sexes, the Prisoners' Dilemma, and the Stag Hunt, is examined. We find that entanglement transforms these dilemmas with each other but cannot resolve them, except in the Stag Hunt game where the dilemma can be alleviated to a certain degree.
Cheon Taksu
Ichikawa Tsubasa
Tsutsui Izumi
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