Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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}\psi\right\rangle =\cos\frac{\xi}%
{2}\left|00\right\rangle +i\sin\frac{\xi}{2}\left|11\right\rangle $ 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\ $\sin\xi>\frac{1}{7}$ with $Q\otimes Q$ as a NE but the quantized game
behaves like PD when $\sin\xi>\frac{1}{3}$; whereas in the range
$\frac{1}{7}<\sin\xi<\frac{1}{3}$ it behaves like chicken game (CG)\ with
$Q\otimes Q$ as a NE. For the measurement in product basis the quantized PD
behaves like classical PD for $\sin^{2}\frac{\xi}{2}<\frac{1}{3}$ with
$D\otimes D$ as a NE. In region $\frac{1}{3}<\sin^{2}\frac{\xi}{2}%
<\frac{3}{7}$ the quantized PD behaves like classical CG with $C\otimes D$ and
$D\otimes C$ as NE.

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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
5
The categories of this paper are: gr-qc