# Network topology design to influence the effects of manipulative behaviors in a social choice procedure

## TL;DR

This paper investigates how designing social network topologies can influence the stability of agents' behaviors in a repeated game, proposing an optimization approach using genetic algorithms to stabilize dynamics.

## Contribution

It introduces a novel network topology design method to stabilize social choice dynamics affected by manipulative behaviors, formulated as a BMI-constrained optimization problem.

## Key findings

- Genetic Algorithm effectively stabilizes social dynamics.
- Network topology impacts agents' stability and manipulation.
- Simulation results validate the proposed approach.

## Abstract

A social choice procedure is modeled as a repeated Nash game between the social agents, who are communicating with each other through a social communication network modeled by an undirected graph. The agents' criteria for this game are describing a trade off between self-consistent and manipulative behaviors. Their best response strategies are resulting in two dynamics rules, one for the agents' opinions and one for their actions. The stability properties of these dynamics are studied. In the case of instability, the stabilization of these dynamics through the design of the network topology is formulated as a constrained integer programming problem. The constraints have the form of a Bilinear Matrix Inequality (BMI), which is known to result in a nonconvex feasible set in the general case. To deal with this problem a Genetic Algorithm is designed. Finally, simulations are presented for several different initial topologies and conclusions are derived concerning both the functionality of the algorithm and the advisability of the problem formulation.