In-Depth Analysis of the Naming Game Dynamics: The Homogeneous Mixing Case

Abstract

Language emergence and evolution has recently gained growing attention through multiagent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding. 15:56 WSPC/INSTRUCTION FILE ng˙long˙ijmpc˙last3 2 Andrea Baronchelli, Vittorio Loreto and Luc Steels telepathy? The problem has been addressed by several disciplines, but it is only in the last decade that there has been a growing effort to tackle it scientifically using multi-agent models and mathematical approaches (cfr. 1,2,3 for a review). Initially these models focused on the emergence of a shared vocabulary, but increasingly attempts are made to tackle grammar 1,4,5,6,7 .The proposed models can be classified as defending a sociobiological or a sociocultural explanation. The sociobiological approach 8 , which includes the evolutionary language game 1 , is based on the assumption that successful communicators, enjoying a selective advantage, are more likely to reproduce than worse communicators. If communication strategies are innate, then more successful strategies will displace rivals. The term strategy acquires its precise meaning in the context of a particular model. For instance, it can be a strategy for acquiring the lexicon of a language, i.e., a function from samplings of observed behaviors to acquired communicative behavior patterns 8,9,10 , or it can simply coincide with the lexicon of the parents 1 or with some strong disposition to acquire a particular kind of syntax, usually called innate Universal Grammar 11 .In this paper we discuss a model, first proposed in 12 , that belongs to the sociocultural family 13,14,15 . Here, good strategies do not necessarily provide higher reproductive success, but only higher communicative success and greater expressive power, and hence greater success in reaching cooperative goals, with less effort. Agents select better strategies exploiting cultural choices, feedback from communication, and a sense of effort. Agents have not only the ability to acquire an existing system but to expand their rules to deal with new communicative challenges and to adjust their rules based on observing the behavior of others. Global coordination emerges over cultural timescales, and language is seen as an evolving and self-organized system 16 . While the sociobiological approach emphasizes language transmission following a vertical, genetic or generational line, the sociocultural approach emphasizes peer-to-peer interaction 17 .A second, fundamental distinction among the different models concerns the adopted mechanisms of social learning describing how stable dispositions are ...

Consensus in networks of mobile communicating agents

“…The agents play the minimal naming game (NG) [25,26] implemented with local broadcasting without feedback [13]. Each agent is characterized by an inventory of words (or "conventions," "opinions," "forms," or "states").…”

On the emergence of semantic agreement among rational agents

“…different values. 7 If the decision analysis results in a 1 as the Bayes action in more than (1 − φ 0 ) percent of agents, then it is impossible to reach an agreement on an acceptable quality of the schema mapping; because in this case, with reference to (1), the proportion of the agents that would prefer to keep and use their current instances of the schema mapping would be too high to achieve a consensus on the quality. Therefore:…”

“…8 A receiving cost is also anticipated in the communication cost, however here, we focus on the sending cost, because this is the dominant cost component. There is also an 7 We experimentally investigate the latter setting in the evaluation section. 8 Such a cost would be reasonable (under rationality assumptions)…”

“…Whereas, in our case, not all the agents necessarily converge to the same semantic mappings, yet they can reach an agreement by establishing a consensus on quality of the schema mapping. In [7], the authors analyze a dynamic model known as the Naming Game and discuss that it is able to account for the distributed coordination of autonomous agents and the emergence of global agreement. Aiming at defining the microscopic behavior of the agents in emergence of shared vocabularies, the authors in [6] study semiotic dynamics of a similar model to [7].…”

“…In [7], the authors analyze a dynamic model known as the Naming Game and discuss that it is able to account for the distributed coordination of autonomous agents and the emergence of global agreement. Aiming at defining the microscopic behavior of the agents in emergence of shared vocabularies, the authors in [6] study semiotic dynamics of a similar model to [7]. They show that the model exhibits the same phenomena as observed in human semiotic dynamics, specifically a period of preparation followed by a rather sharp transition into global…”