Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

We investigate a simply evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the payoff b of a defector exploiting a cooperator is small. Furthermore, if b is larger enough, the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is estimated roughly. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.