  We present a detailed study of prisoner's dilemma game with stochastic
modifications on a two-dimensional lattice, in presence of evolutionary
dynamics. By very nature of the rules, the cooperators have incentive to cheat
and the fear to being cheated in prisoner's dilemma and may cheat even when not
dictated by evolutionary dynamics. We consider two variants. In either case,
the agents mimic the action (cooperation or defection) in the previous timestep
of the most successful agent in the neighborhood. Over and above this, the
fraction p of cooperators spontaneously change their strategy to pure defector
at every time step in the first variant. In the second variant, there are no
pure cooperators. All cooperators keep defecting with probability p at every
time-step. In both cases, the system switches from coexistence state to an
all-defector state for higher values of p. We show that the transition between
these states unambiguously belongs to directed percolation universality class
in 2 + 1 dimension. We also study the local persistence and the persistence
exponents are higher than ones obtained in previous studies underlining their
dependence on details of dynamics
