Modelling the Prisoner’s Dilemma (I).
(a) Graphical representation of the connectivity pattern Π(λa) defined in Eq. (6). The connected component in red color corresponds to the dynamic comparison of the two possible actions when expecting the opponent to cooperate and the blue one represents the same process under the belief of receiving defection from the other player. With the only purpose of clarifying the structure of the matrix Π, the process of formation of beliefs is depicted just symbolically through the green links. (Note that we don’t show the self-edges). Because of the symmetry in the game, the components of the matrix B(λb) can be related to those of Π, as we can see in Eq. (7) and the corresponding discussion in the main text. Panel (b) illustrates (for a fixed value of φ = 0.2) how the probability of choosing the action of defection increases with the rationality parameter λ. Panel (c) illustrates the probability of defection (for a fixed value of λ = 10) as a function of α and φ. See discussion in the main body of the text.