Convergence to shared lexicons for multi-object domains

Abstract

In recent years, consensus problems have attracted increasing attention from researchers in various fields. Consensus problems in language emergence and evolution are always raised in the following form: how might a group of agents reach a shared communication system under certain patterns of interaction despite the absence of a centralized coordinator? In this thesis, consensus problems of a multi-agent model for multi-object domains in discrete time are considered. We first propose a generalization of Liberman’s model and study how a group of agents produce a common lexicon to describe the same collection objects despite their different initial beliefs on word usage. At each time, all agents meet together, select an object, exchange messages with a name for this object, and update their beliefs, based on these messages, according to a designed protocol. We study the dynamics for this model and analyze convergence and homonymy phenomena. Then we study a different situation on which each agent can select its own individual object. In contrast with the previous case, however, we now assume that agents can exchange their beliefs (instead of only pairs (object, word)). We prove that all beliefs will converge to the same belief provided each object is selected frequently enough. Finally, computer simulations are attached to support the mathematical proofs of the above two cases.