Global dynamics in adaptive models of collective choice with social influence

In this chapter we present a unified approach for modelling the diffusion of alternative choices within a population of individuals in the presence of social externalities, starting from two particular discrete-time dynamic models Galam's model of rumors spreading [10] and a formalization of Schelling's binary choices [7]. We describe some peculiar properties of discrete-time (or event-driven) dynamic processes and we show how some long-rum (asymptotic) outcomes emerging from repeated short time decisions can be seen as emerging properties, sometimes unexpected, or difficult to be forecasted