# Game-Theoretic Analysis of the Hegselmann-Krause Model for Opinion Dynamics in Finite Dimensions

@article{Etesami2015GameTheoreticAO, title={Game-Theoretic Analysis of the Hegselmann-Krause Model for Opinion Dynamics in Finite Dimensions}, author={Seyed Rasoul Etesami and Tamer Başar}, journal={IEEE Transactions on Automatic Control}, year={2015}, volume={60}, pages={1886-1897} }

We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions and show that the termination time in general only depends on the number of agents involved in the dynamics. To the best of our knowledge, that is the sharpest bound for the termination time of such dynamics that removes dependency of the termination time from…

## 123 Citations

### How friends and non-determinism affect opinion dynamics

- Mathematics2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

It is proved that, for any fixed ε > 0, both these systems make only a polynomial number of steps in which two agents separated by distance at least ε interact with each other, regardless of the social network in the first variant and with only a bound on the noise in the second.

### Mixed Hegselmann-Krause Dynamics--Nondeterministic Case

- Mathematics
- 2021

The original Hegselmann-Krause (HK) model is composed of a finite number of agents characterized by their opinion, a number in [0, 1]. An agent updates its opinion via taking the average opinion of…

### Hegselmann-Krause Opinion Dynamics in Finite Dimensions

- Mathematics
- 2017

In this chapter we describe the discrete-time Hegselmann-Krause opinion dynamics model as introduced in [1], and study its termination time under various scenarios. Despite many works and efforts…

### Partial convergence of heterogeneous Hegselmann-Krause opinion dynamics

- Mathematics
- 2016

A partial convergence conclusion of the general heterogeneous HK dynamics is proved, that is, there must be some agents who will reach static states in finite time, while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.

### Probability of Consensus of Hegselmann-Krause Dynamics

- Mathematics
- 2021

The original Hegselmann-Krause (HK) model comprises a set of n agents characterized by their opinion, a number in [0, 1]. Agent i updates its opinion xi via taking the average opinion of its…

### Tuning Cooperative Behavior in Games With Nonlinear Opinion Dynamics

- EconomicsIEEE Control Systems Letters
- 2022

This work examines the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics and shows how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas.

### Multi-dimensional extensions of the Hegselmann-Krause model

- MathematicsArXiv
- 2022

—In this paper we consider two multi-dimensional Hagselmann-Krause (HK) models for opinion dynamics. The two models describe how individuals adjust their opinions on multiple topics, based on the…

### The discrete-time Altafini model of opinion dynamics with communication delays and quantization

- Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

Modified versions of the Altafini model in which there are communication delays or quantized communication are studied, showing that in finite time and depending on initial conditions, the model will either cause all agents to reach a quantized consensus in absolute value, or will lead all variables to oscillate in a small neighborhood around the absolute value.

### Heterogeneous Hegselmann–Krause Dynamics With Environment and Communication Noise

- MathematicsIEEE Transactions on Automatic Control
- 2020

The results reveal that the heterogeneity of individuals is harmful to synchronization, which may be the reason why the synchronization of opinions is hard to reach in reality, even within that of a small group.

### An approximation algorithm and price of anarchy for the binary-preference capacitated selfish replication game

- Economics, Computer Science2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

A quasi-polynomial algorithm O(n2+ln D) is devised which can find an allocation profile that is within a constant factor of the optimal allocation, and hence of any pure-strategy Nash equilibrium of the game.

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