Combinatorial Naming Game

Si Yuan Guo

Shared Vocabulary

How large populations converge to a shared vocabulary without global coordination?

• innate knowledge?

• group dynamics of agents ?

Naming Game

•each agent has an inventory of words, Wi

•all agents face a same set of objects, O

•each agent have a dictionary of vocabulary, Vi

•a set of agents, A, interact with each other (two at a time) and update their vocabularies, Vi

From: Baronchelli, A., & Felici, M. (2006). Sharp transition towards shared vocabularies in multi-agent systems. Journal

of Statistical Physics.

How agents interact: a minimal strategy

Combinatorial Naming Game

•Duality of Patterning, Hockett (1960):

• combinatoriality: [k]+[æ]+[t] = “cat”

• compositionality: “meaning”+“less” = “meaningless”

When and how to combine?

•size of phonemeInventory < size of objects

•phonemeInventory is used up

•when inventing word, avoid using used word

a problem: homonym

• multiple objects have the same name

• when there are only 2 agents, no homophones

• the number of homophone will grow sharply with population size and finally become relatively stable.

Will the size of phoneme inventory change the dynamics

of homonym?

darker green lines = more initial phonemes

phonemeInventory = [2,4,8,16], objects = 8,

population = [2,4,8,16,32]

Will the social structures of agents change the dynamics of

homonym?

• default method = complete graph

• what about a tree graph?

• circle graph?

• scale-free(Barabasi-Albert) graph?

objects:8; populations:[2,4,8,16,32,64]; social structure: •black: complete graph•green: tree graph•blue: circle graph•red: scale-free graph

• Changes of social structures of agents seem cannot help much.• Additional strategies(interacting rules) should be implemented.

Next step

• Is there a more realistic way to combine phonological units into larger units?

• Do languages really start from a set of undividable smallest units, or there is a holistic stage where a set of smallest units emerge from? If so, why and how do they emerge?