  A simplified prisoner's game is studied on a square lattice when the players
interacting with their neighbors can follow only two strategies: to cooperate
(C) or to defect (D) unconditionally. The players updated in a random sequence
have a chance to adopt one of the neighboring strategies with a probability
depending on the payoff difference. Using Monte Carlo simulations and dynamical
cluster techniques we study the density $c$ of cooperators in the stationary
state. This system exhibits a continuous transition between the two absorbing
state when varying the value of temptation to defect. In the limits $c \to 0$
and 1 we have observed critical transitions belonging to the universality class
of directed percolation.
