### Abstract

In this article we study a biased version of the naming game in which players are located on a connected graph and interact through successive conversations in order to select a common name for a given object. Initially, all the players use the same word B except for one bilingual individual who also uses word A. Both words are attributed a fitness, which measures how often players speak depending on the words they use and how often each word is spoken by bilingual individuals. The limiting behavior depends on a single parameter, ∅, denoting the ratio of the fitness of word A to the fitness of word B. The main objective is to determine whether word A can invade the system and become the new linguistic convention. From the point of view of the mean-field approximation, invasion of word A is successful if and only if ∅ > 3, a result that we also prove for the process on complete graphs relying on the optimal stopping theorem for supermartingales and random walk estimates. In contrast, for the process on the one-dimensional lattice, word A can invade the system whenever ∅ > 1.053, indicating that the probability of invasion and the critical value for ∅ strongly depend on the degree of the graph. The system on regular lattices in higher dimensions is also studied by comparing the process with percolation models.

Original language | English (US) |
---|---|

Pages (from-to) | 139-158 |

Number of pages | 20 |

Journal | Journal of Applied Probability |

Volume | 51A |

State | Published - Dec 1 2014 |

### Fingerprint

### Keywords

- Interacting particle system
- Language dynamics
- Naming game
- Semiotic dynamics

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Applied Probability*,

*51A*, 139-158.

**The naming game in language dynamics revisited.** / Lanchier, Nicolas.

Research output: Contribution to journal › Article

*Journal of Applied Probability*, vol. 51A, pp. 139-158.

}

TY - JOUR

T1 - The naming game in language dynamics revisited

AU - Lanchier, Nicolas

PY - 2014/12/1

Y1 - 2014/12/1

N2 - In this article we study a biased version of the naming game in which players are located on a connected graph and interact through successive conversations in order to select a common name for a given object. Initially, all the players use the same word B except for one bilingual individual who also uses word A. Both words are attributed a fitness, which measures how often players speak depending on the words they use and how often each word is spoken by bilingual individuals. The limiting behavior depends on a single parameter, ∅, denoting the ratio of the fitness of word A to the fitness of word B. The main objective is to determine whether word A can invade the system and become the new linguistic convention. From the point of view of the mean-field approximation, invasion of word A is successful if and only if ∅ > 3, a result that we also prove for the process on complete graphs relying on the optimal stopping theorem for supermartingales and random walk estimates. In contrast, for the process on the one-dimensional lattice, word A can invade the system whenever ∅ > 1.053, indicating that the probability of invasion and the critical value for ∅ strongly depend on the degree of the graph. The system on regular lattices in higher dimensions is also studied by comparing the process with percolation models.

AB - In this article we study a biased version of the naming game in which players are located on a connected graph and interact through successive conversations in order to select a common name for a given object. Initially, all the players use the same word B except for one bilingual individual who also uses word A. Both words are attributed a fitness, which measures how often players speak depending on the words they use and how often each word is spoken by bilingual individuals. The limiting behavior depends on a single parameter, ∅, denoting the ratio of the fitness of word A to the fitness of word B. The main objective is to determine whether word A can invade the system and become the new linguistic convention. From the point of view of the mean-field approximation, invasion of word A is successful if and only if ∅ > 3, a result that we also prove for the process on complete graphs relying on the optimal stopping theorem for supermartingales and random walk estimates. In contrast, for the process on the one-dimensional lattice, word A can invade the system whenever ∅ > 1.053, indicating that the probability of invasion and the critical value for ∅ strongly depend on the degree of the graph. The system on regular lattices in higher dimensions is also studied by comparing the process with percolation models.

KW - Interacting particle system

KW - Language dynamics

KW - Naming game

KW - Semiotic dynamics

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UR - http://www.scopus.com/inward/citedby.url?scp=84918546943&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84918546943

VL - 51A

SP - 139

EP - 158

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

ER -