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The Prisoner's Dilemma (PD) game is used in several fields due to theemergence of cooperation among selfish players. Here, we have considered aone-dimensional lattice, where each cell represents a player, that cancooperate or defect. This one-dimensional geometry allows us to retrieve theresults obtained for regular lattices and to keep track of the systemspatio-temporal evolution. Players play PD with their neighbors and updatetheir state using the Pavlovian Evolutionary Strategy. If the players receive apositive payoff greater than an aspiration level, they keep their states andswitch them, otherwise. We obtain analitycally the critical temptation values,we present the cluster patterns that emerge from the players local interactionand we perform an exploration of paramater space. The numerical results are inaccordance to the critical temptation analitycal results, it confirms that thePavlovian strategy foment the cooperation among the players and avoid thedefection. The system also presented a new phase in the steady state, thequasi-regular phase, where several players switch their states during round toround, but the proportion of cooperators does not alter significantly.

Pavlovian Prisoner's Dilemma in one-dimensional cellular automata:  analytical results, the quasi-regular phase, spatio-temporal patterns and  parameter space exploration