The paper studies the evolutionary prisoner's dilemma game on a square lattice, where players can either cooperate (C) or defect (D) unconditionally. The players update their strategies randomly, adopting one of their neighbors' strategies with a probability based on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, the density of cooperators in the stationary state is analyzed. The system exhibits a continuous transition between two absorbing states (all D or all C) as the temptation to defect varies. Critical transitions are observed at the limits of zero and one cooperators, belonging to the universality class of directed percolation. The study also explores the impact of noise levels on the density of cooperators and the behavior of cooperators and defectors in the coexistence region. The results show that the presence of noise reduces the active region and affects the threshold values for stable cooperation. The generalized mean-field approximations highlight the importance of short-range correlations, while Monte Carlo simulations reveal power-law behavior in the critical regions. The findings support the conjecture that transitions to absorbing states in one-component models belong to the directed percolation universality class.The paper studies the evolutionary prisoner's dilemma game on a square lattice, where players can either cooperate (C) or defect (D) unconditionally. The players update their strategies randomly, adopting one of their neighbors' strategies with a probability based on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, the density of cooperators in the stationary state is analyzed. The system exhibits a continuous transition between two absorbing states (all D or all C) as the temptation to defect varies. Critical transitions are observed at the limits of zero and one cooperators, belonging to the universality class of directed percolation. The study also explores the impact of noise levels on the density of cooperators and the behavior of cooperators and defectors in the coexistence region. The results show that the presence of noise reduces the active region and affects the threshold values for stable cooperation. The generalized mean-field approximations highlight the importance of short-range correlations, while Monte Carlo simulations reveal power-law behavior in the critical regions. The findings support the conjecture that transitions to absorbing states in one-component models belong to the directed percolation universality class.