This book provides a gradual introduction to the naming game, starting from the minimal naming game, where the agents have infinite memories (Chapter 2), before moving on to various new and advanced settings: the naming game with agents possessing finite-sized memories (Chapter 3); the naming game with group discussions (Chapter 4); the naming game with learning errors in communications (Chapter 5) ; the naming game on multi-community networks (Chapter 6) ; the naming game with multiple words or sentences (Chapter 7) ; and the naming game with multiple languages (Chapter 8). Presenting the authors' own research findings and developments, the book provides a solid foundation for future advances. This self-study resource is intended for researchers, practitioners, graduate and undergraduate students in the fields of computer science, network science, linguistics, data engineering, statistical physics, social science and applied mathematics.

It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject.