## Abstract

A long-standing line of work in economic theory has studied models by which a group of people in a social network, each holding a numerical opinion, can arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that consensus is rarely reached in real opinion dynamics, we study a related sociological model in which individuals' intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions. By interpreting the repeated averaging as best-response dynamics in an underlying game with natural payoffs, and the limit of the process as an equilibrium, we are able to study the cost of disagreement in these models relative to a social optimum. We provide a tight bound on the cost at equilibrium relative to the optimum, our analysis draws a connection between these agreement models and extremal problems for generalized eigenvalues. We also consider a natural network design problem in this setting, where adding links to the underlying network can reduce the cost of disagreement at equilibrium.

Original language | English |
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Title of host publication | Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |

Pages | 57-66 |

Number of pages | 10 |

DOIs | |

State | Published - 1 Dec 2011 |

Externally published | Yes |

Event | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States Duration: 22 Oct 2011 → 25 Oct 2011 |

### Conference

Conference | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |
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Country/Territory | United States |

City | Palm Springs, CA |

Period | 22/10/11 → 25/10/11 |

## Keywords

- Algorithmic Game Theory
- DeGroot Model
- Social Networks