Analyzing the opinion dynamics models discrete & continuous

In this thesis we analyze some of the opinion dynamics in both discrete and continuous cases. In the discrete case, we will find some criteria under which we can say more about the behavior of the dynamics such as convergence of the agents to the same opinion, or consensus. For this purpose, we first consider the agent-based bounded confidence model of the Hegselmann-Krause where multiple agents want to agree on a common scalar, or they can be divided in several subgroups, with each subgroup having its own agreement value. In this model, we restrict ourselves to the case when all the agents have the same bound of confidence, often referred to as homogeneous case. We are interested to study the number of iterations which is enough for the termination of the Hegselmann-Krause algorithm. In other words, we want to give an upper bound on the number of iterations which guarantees the termination of the algorithm independently of reaching a consensus or not. Assuming the consensus is achieved in the Hegselmann-Krause model, we first give an upper bound on the number of iterations and then we provide another upper bound without any assumption. In chapter 3 we use some analysis based on Lyapunov function theory to improve our upper bound substantially. In our analysis we use two differnt type of Lyapunov functions which each of them gives us a polynomial upper bound for the termination time. In chapter 4 we consider the Hegselmann-Krause model in higher dimensions. We will see that in higher dimensions we don’t have lots of nice properties which exist in the scalar case. Then, we will find some upper bounds for the termination time. Also, at the end we will consider an extension of the Hegselmann-Krause model to continuous case such that the time is discrete but the density of the agents is continuous over the real line. In chapter 5 we use the matrix representation for the discrete dynamics and we provide some conditions on a chain of stochastic matrices based on their decomposition by permutation matrices such that it can guarantee the convergence of the chain to a consensus matrix. Also, we provide some examples and one necessary condition for finite time convergence of an especial case of averaging gossip algorithms.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Industrial Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Etesami, Seyed Rasoul

Contributors dc:contributor

• Nedich, Angelia

• Hegselmann-Krause

Statement dc:rights

• Copyright 2012 Seyed Rasoul Etesami

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/31120

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31120