Topology-induced coarsening in language games

Abstract

We investigate how very large populations are able to reach a global consensus, out of local "microscopic" interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called Naming Game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low-dimensions consensus is reached through a coarsening process which requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In 1-d the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N 1+2/d in dimension d ≤ 4 (the upper critical dimension), while in mean-field both memory and time scale as N 3/2 , for a population of N agents. We present analytical and numerical evidences supporting this picture.The past decade has seen an important development of the so-called Semiotic Dynamics, a new field which studies how conventions (or semiotic relations) can originate, spread and evolve over time in populations. This occurred mainly trough the definition of Language interaction games [1,2] in which a population of agents is seen as a complex adaptive system which self-organizes [3] as a result of simple local interactions (games). The interest of physicists for Language Games comes from the fact that they can be easily formulated as non-equilibrium statistical mechanics models of interacting agents: at each time step, an agent updates its state (among a certain set of possible states) through an interaction with its neighbors. An interesting question concerns the possibility of convergence towards a common state for all agents, which emerges without external global coordination and from purely local interaction rules [4,5,6]. In this Letter, we focus on the so-called Naming Games, introduced to describe the emergence of conventions and shared lexicons in a population of individuals interacting with each other by negotiations rules, and study how the embedding of the agents on a low-dimensional lattice influences the emergence of consensus, which we show to be reached through a coarsening process. The original model [7] was inspired by a well-known experiment of artificial intelligence called Talking Heads [8], in which embodied software agents develop their vocabulary observing objects through digital cameras, assigning them randomly chosen names and negotiating these names with other agents.Recently a new minimal version of the Naming Game endowed with simplified interactions rules [9] has been introduced, that reproduces the phenomenology of the experiments and is amenable to analytical treatment. In this model, N individuals (or agents) observe the same object, trying to communicate its name one to the other.

The spontaneous emergence of conventions: An experimental study of cultural evolution

“…Theoretical predictions for our study are based on a derived "language game" model of convention formation (27), in which agents attempting to coordinate in pairwise interactions accrue a memory of past plays, which they use to "guess" the words that will be used by their subsequent partners (Model). Consistent with a broad range of formal approaches (5,33,(42)(43)(44), this model predicts that the connectivity of the actors' social networks can influence the collective dynamics of convention formation, ranging from the emergence of competing regional norms that inhibit global coordination (45) to the rapid growth of universally shared social conventions (27) (Model). We evaluated these predictions by studying convention formation in three representative network configurations: (i) spatially embedded social topologies (i.e., one-dimensional lattices with degree 4) (45,46,47), (ii) randomly connected topologies (i.e., random graphs with constant degree 4) (42,48), and (iii) homogeneously mixing populations (3,27).…”

“…3 shows the changing distribution of popularity among the competing alternatives in all Early in the evolutionary process, all networks exhibited a broad distribution of active alternatives, indicating that even the least popular options had nontrivial representation within the population. However, as the ecologies evolved, the distribution of alternatives in the spatially embedded and randomly connected populations became increasingly exponential, producing an emergent "oligopoly," in which a few entrenched local conventions eliminated all other alternatives (45,52). Each of these conventions competed for ground against the others, but none of them assumed the majority.…”

“…As shown in Fig. 2, behavior in the spatial networks evolved through a process of local coarsening (45), in which emergent regions of coordinated behavior competed with bordering local conventions (45,49,50). In each of the trials, these dynamics inhibited the spontaneous emergence of global coordination by creating entrenched competition between endogenously formed groups (51).…”

Agreement dynamics on interaction networks with diverse topologies

“…[19]. When the interacting agents sit on the nodes of lowdimensional lattices, the long-time behavior is still characterized by the convergence to a homogeneous consensus state, but the evolution of the system changes considerably.…”

“…In this article, we review the behaviour of a recently proposed model for the emergence of a communication system, called Naming Game, investigating its dynamical behavior on both regular topologies and complex networks [19][20][21][22]. Social interactions are indeed based on the existence of a communication system among the agents, who are able to understand each other by means of common linguistic patterns or, more generally, by means of a common vocabulary of symbols.…”