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 for PD in Markov strategies and the QRE curve.