Advances in Complex Systems

The paper investigates the dynamical properties of spatially distributed naming games. Naming games are interactions between two agents, a speaker and a hearer, in which the speaker identifies an object using a name. Adaptive naming games imply that speaker and hearer update their lexicons to become better in future games. By engaging in adaptive naming games, a coherent shared vocabulary arises through self-organisation in a population of distributed agents. When the agents are spatially distributed, diversity can be shown to arise, and changes, in population contact lead to language changes.

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.

We propose that a regulation mechanism based on Hebbian covariance plasticity may cause the brain to operate near criticality. We analyze the effect of such a regulation on the dynamics of a network with excitatory and inhibitory neurons and uniform connectivity within and across the two populations. We show that, under broad conditions, the system converges to a critcal state lying at the common boundary of three regions in parameter space; these correspond to three modes of behavior: high activity, low activity, oscillation.