Physica A 478 (2017) 177–187 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Asymptotic properties of restricted naming games Biplab Bhattacherjee a , Amitava Datta b , S.S. Manna a,∗ a Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700106, India b School of Computer Science and Software Engineering, University of Western Australia, Perth, WA 6009, Australia highlights • Naming games are studied with finite sizes of the agent vocabularies. • Naming games are studied with limited number of distinct names. • Different dynamical rules lead to different new power law exponents. article info Article history: Received 16 October 2016 Received in revised form 16 February 2017 Available online 28 February 2017 Keywords: Naming games Self-organized systems Scaling Critical exponents Structures and organization in complex systems Critical phenomena abstract Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games. © 2017 Elsevier B.V. All rights reserved. 1. Introduction The aim of the model of naming game is to study the evolution of consensus opinion in the context of naming a single object in a large community of agents [1,2]. Different agents refer to the object using different names when the object is introduced initially. Agents interact among themselves and share the names that have been already introduced according to a set of specific rules. At the early stage, the number of distinct names for the object increases as the agents introduce new names for the object. However as the game progresses, a consensus name gradually emerges and distinct names disappear. The dynamical evolution of the game terminates when all agents agree upon a single name through mutual interactions and following the rules of the game. At an arbitrary intermediate stage, an agent has a number of names of the same object in his vocabulary suggested by different groups of agents. An agent, under the sharing dynamics, not only learns new names for the object but also shares names from his own vocabulary with other agents. In the models studied for the dynamics of naming games in the literature, the sizes of the vocabularies of the agents have been assumed to be infinite [3–10]. Real world data in this problem ∗ Corresponding author. E-mail address: manna@bose.res.in (S.S. Manna). http://dx.doi.org/10.1016/j.physa.2017.02.070 0378-4371/© 2017 Elsevier B.V. All rights reserved.