  The study of the nature of human cooperation still contains gaps needing
investigation. Previous findings reveal that socialization effectively promotes
cooperation in the well-known Prisoner's dilemma (PD) game. However,
theoretical concepts fail to describe high levels of cooperation (probability
higher than 50%) that were observed empirically. In this paper, we derive a
symmetrical quantal response equilibrium (QRE) in PD in Markov strategies and
test it against experimental data. Our results indicate that for low levels of
rationality, QRE manages to describe high cooperation. In contrast, for high
rationality QRE converges to the Nash equilibrium and describes low-cooperation
behavior of participants. In the area of middle rationality, QRE matches the
curve that represents the set of Nash equilibrium in Markov strategies.
Further, we find that QRE serves as a dividing line between behavior before and
after socialization, according to the experimental data. Finally, we
successfully highlight the theoretically-predicted intersection of the set of
Nash equilibrium in Markov strategies and the QRE curve.
