Emergence of fast agreement in an overhearing population: The case of the naming game

The naming game (NG) describes the agreement dynamics of a population of N agents interacting locally in pairs leading to the emergence of a shared vocabulary. This model has its relevance in the novel fields of semiotic dynamics and specifically to opinion formation and language evolution. The application of this model ranges from wireless sensor networks as spreading algorithms, leader election algorithms to user-based social tagging systems. In this paper, we introduce the concept of overhearing (i.e., at every time step of the game, a random set of N-delta individuals are chosen from the population who overhear the transmitted word from the speaker and accordingly reshape their inventories). When delta = 0 one recovers the behavior of the original NG. As one increases delta, the population of agents reaches a faster agreement with a significantly low-memory requirement. The convergence time to reach global consensus scales as log N as delta approaches 1. Copyright (C) EPLA, 2013