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Generating social networks with static and dynamic utility-maximization approaches

Aldric Labarthe, Yann Kerzreho

TL;DR

A conceptual framework that model human social networks as an undirected dot-product graph of independent individuals, which enables social scientists to perform an in-depth analysis of the consequences of behavioral constraints affecting individuals on the network they form is introduced.

Abstract

In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an objective function at the scale of the individual or of the whole network. On this framework, we build a new artificial network generator in two versions. The first fits within the tradition of artificial network generators by being able to generate similar networks from empirical data. The second relaxes the computational efficiency constraint and implements the same micro-based decision algorithm, but in agent-based simulations with time and fully independent agents. This latter version enables social scientists to perform an in-depth analysis of the consequences of behavioral constraints affecting individuals on the network they form. This point is illustrated by a case study of imperfect information.

Generating social networks with static and dynamic utility-maximization approaches

TL;DR

A conceptual framework that model human social networks as an undirected dot-product graph of independent individuals, which enables social scientists to perform an in-depth analysis of the consequences of behavioral constraints affecting individuals on the network they form is introduced.

Abstract

In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an objective function at the scale of the individual or of the whole network. On this framework, we build a new artificial network generator in two versions. The first fits within the tradition of artificial network generators by being able to generate similar networks from empirical data. The second relaxes the computational efficiency constraint and implements the same micro-based decision algorithm, but in agent-based simulations with time and fully independent agents. This latter version enables social scientists to perform an in-depth analysis of the consequences of behavioral constraints affecting individuals on the network they form. This point is illustrated by a case study of imperfect information.

Paper Structure

This paper contains 15 sections, 14 theorems, 26 equations, 4 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Conceptual Framework
  4. Optimal Graph generation: a social optimization
  5. Decentralized graph generation: an agent-based model
  6. Simulation methodology
  7. Results
  8. Similar networks generation
  9. Decentralized optimization and agent-based model
  10. Discussion
  11. Theoretical and mathematical Framework
  12. Fundamental definitions
  13. A network optimization problem
  14. Alky utility function
  15. Detailed algorithms for the agent-based model

Key Result

Theorem 1

For any $\mathcal{G}(\mathscr{I} , \alpha, C)$, the Social Optimization Problem has only one unique solution.

Figures (4)

  • Figure 1: Methodology to generate similar networks or perfect clones of a real network
  • Figure : Individual $i$ select action protocol (simplified)
  • Figure : Individual $i$ select action protocol (Detailed)
  • Figure : Simulation body (detailed)

Theorems & Definitions (42)

  • Definition 1: Individuals space
  • Definition 2: Individuals graph
  • Definition 3: ALKY utility function
  • Remark 1
  • Definition 4: Social Optimization Problem
  • Theorem 1: Unicity of the optimal graph
  • Theorem 2
  • Definition 5: Individual Optimization Problem
  • Theorem 3: Unicity of the individual optimal graph
  • Theorem 4: Invisible hand
  • ...and 32 more