We present extensive numerical simulations of the Axelrod's model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytical findings.

We use a stochastic description of models with a dynamic in quenched disorder to analyze the mechanism of their self-organization to a critical state in terms of memory effects. We introduce a framework to characterize both memory effects and avalanche events which suggests that self-organization can result in general from memory. This issue is settled by the introduction and the analysis of a model that contains explicitly memory and generalizes the corresponding dynamics in quenched disorder. The model displays a rich behavior and self-organized critical properties for a whole range of the exponent that tunes the strength of memory. © 1996 The American Physical Society.

We show that the minority game, a model of interacting heterogeneous agents, can be described as a spin system and displays a phase transition between a symmetric phase and a symmetry broken phase where the game’s outcome is predictable. As a result a “spontaneous magnetization” arises in the spin formalism.