Can stubbornness or gullibility lead to faster consensus? A study of various strategies for reaching consensus in a model of the naming game

The naming game is a dynamical system that is used to model and study language formation, in particular to determine how words are formed that are used by all members of a community to denote the same object or concept. We propose a model of the naming game that allows for theoretical investigation under various behavior for agent interaction. In particular, we give conditions on the network such that consensus is reached where at most p synonyms are used to describe a single object. In addition, we give lower bounds on the convergence rate to consensus. Furthermore, we study various agent interaction behaviors and their effect on the time needed to reach consensus. We show that even though a democratic strategy is in general the best strategy for reaching consensus, a stubborn or a gullible strategy can allow for faster word formation than a democratic strategy for certain connection topologies among the agents.

[1]  Andrea Baronchelli,et al.  Microscopic activity patterns in the Naming Game , 2006, ArXiv.

[2]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[3]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[4]  Vittorio Loreto,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Sharp transition towardsshared vocabularies in multi-agent systems , 2006 .

[5]  Chai Wah Wu.  Agreement and consensus problems in groups of autonomous agents with linear dynamics , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[6]  J. A. Fax.  Optimal and Cooperative Control of Vehicle Formations , 2002 .

[7]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[8]  V. Loreto,et al.  The role of topology on the dynamics of the Naming Game , 2007 .

[9]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[10]  Randy Beard,et al.  Information consensus in distributed multiple vehicle coordinated control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Chai Wah Wu,et al.  Conditions for weak ergodicity of inhomogeneous Markov chains , 2008 .

[12]  A. Paz,et al.  Ergodic theorems for sequences of infinite stochastic matrices , 1967, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  Ming Cao,et al.  Topology design for fast convergence of network consensus algorithms , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[14]  M. Bartlett,et al.  Weak ergodicity in non-homogeneous Markov chains , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.