Emergence of cooperation in phenotypically heterogeneous populations: A replicator dynamics analysis
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The emergence of cooperation is analyzed in heterogeneous populations where two kinds of individuals exist according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type. Individuals thus behave under partial information conditions. The interactions between individuals are described by the snowdrift game, where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game theory by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that the four monomorphic states are unstable and that a polymorphic state exists which is a global attractor for non-degenerate initial states of the population. The result for the discrete-time replicator coincides with the one of the continuous case.