title: Pavlovian Prisoner's Dilemma-Analytical results, the quasi-regular phase and spatio-temporal patterns.
abstract: The Prisoner's Dilemma (PD) game is applied in several research fields due to the emergence of cooperation among selfish players. In this work the PD is studied in a one-dimensional lattice, where each cell represents a player, which in turn can interact with the neighbors playing the PD (cooperate or defect). The update of states adopts the Pavlovian Evolutionary Strategy (PES) or Darwinian Evolutionary Strategy (DES). Adopting PES, if a player receives a positive payoff greater than his/her aspiration level, he/she keeps the current state, and switches otherwise. Adopting DES, player compares his/her payoff with payoff of opponents. If it is not the highest, he/she copies the state of fittest player, switching the state if it is different of his/her current state. The critical temptation values obtained analytically are reported, and the cluster patterns that emerge from the interactions among the players are shown. Also we defined analytical functions that calculate the maximum/minimum size of defective/cooperative clusters. Also, the parameter space is explored with exhaustive computational simulations, which confirm the analytical results and reinforce that Pavlovian strategy foments cooperation among players. In steady state, system can reach the cooperative or quasi-regular phases, when adopting the PES, and cooperative, defective or chaotic phases, adopting the DES. The new quasi-regular phase occurs when several players switch their states in each round, but the proportion of cooperators does not show significant variation. Additionally, the present work shows that the lowest temptation level (T=1) may be considered a trivial case only for the particular case where the players interact with only one neighbor, otherwise system presents the same features that for higher temptation values.
authors.affiliation: Universidade de São Paulo - Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Av. Bandeirantes, 3900, 14040-901 Ribeirão Preto, São Paulo, Brazil. marceloapereira@usp.br
authors.forename: Marcelo Alves
authors.initials: MA
authors.lastname: Pereira
authors.forename: Alexandre Souto
authors.initials: AS
authors.lastname: Martinez
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical