The strategic form of quantum prisoners' dilemma

In its normal form prisoners' dilemma (PD) is represented by a payoff matrix showing players strategies and payoffs. To obtain distinguishing trait and strategic form of PD certain constraints are imposed on the elements of its payoff matrix. We quantize PD by generalized quantization scheme to analyze its strategic behavior in quantum domain. The game starts with general entangled state of the form left}ψrightrangle =cosfracξ% {2}left|00rightrangle +isinfracξ{2}left|11rightrangle and the measurement for payoffs is performed in entangled and product bases. We show that for both measurements there exist respective cutoff values of entanglement of initial quantum state up to which strategic form of game remains intact. Beyond these cutoffs the quantized PD behaves like chicken game up to another cutoff value. For the measurement in entangled basis the dilemma is resolved for\ sinξ>frac{1}{7} with Qotimes Q as a NE but the quantized game behaves like PD when sinξ>frac{1}{3}; whereas in the range frac{1}{7}<sinξ<frac{1}{3} it behaves like chicken game (CG)\ with Qotimes Q as a NE. For the measurement in product basis the quantized PD behaves like classical PD for sin²fracξ{2}<frac{1}{3} with Dotimes D as a NE. In region frac{1}{3}<sin²fracξ{2}% <frac{3}{7} the quantized PD behaves like classical CG with Cotimes D and Dotimes C as NE.