tarting from a seminal paper of Thomas Schelling (1969) we formalize a twodimensional discrete time dynamical system to study segregation. The simple adaptive mechanism we propose may lead to the segregation of two different populations whose members are characterized by a limited tolerance about the presence of individuals of the other group. We provide a global analysis of the model, based on a computerassisted interplay of analytical, numerical and geometrical methods. This allows us to emphasize the role of the parameters that represent the distribution of tolerance within the populations and their inertia in moving in or out of the system considered, as well as the role of constraints imposed. When several attractors are present, each with its own basin of attraction, the adaptive dynamics can act as a path-dependent selection device, i.e., the collective behavior that prevails in the long run depends on the starting conditions and on the historical accidents occurring along the trajectories. The study shows how simple adaptive rules, repeatedly applied over time, can be used to analyze the evolutive paths leading to the emergence of different collective behaviors in the long run, i.e., the trade-off between myopic individual behavior and the emergence of social structures.
An adaptive dynamic model of segregation
BISCHI, GIAN ITALO;
2011
Abstract
tarting from a seminal paper of Thomas Schelling (1969) we formalize a twodimensional discrete time dynamical system to study segregation. The simple adaptive mechanism we propose may lead to the segregation of two different populations whose members are characterized by a limited tolerance about the presence of individuals of the other group. We provide a global analysis of the model, based on a computerassisted interplay of analytical, numerical and geometrical methods. This allows us to emphasize the role of the parameters that represent the distribution of tolerance within the populations and their inertia in moving in or out of the system considered, as well as the role of constraints imposed. When several attractors are present, each with its own basin of attraction, the adaptive dynamics can act as a path-dependent selection device, i.e., the collective behavior that prevails in the long run depends on the starting conditions and on the historical accidents occurring along the trajectories. The study shows how simple adaptive rules, repeatedly applied over time, can be used to analyze the evolutive paths leading to the emergence of different collective behaviors in the long run, i.e., the trade-off between myopic individual behavior and the emergence of social structures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
