The norm game on a model network: a critical line

TL;DR

This paper analyzes the critical conditions under which social norms persist or break down in a network model, highlighting the influence of consistent punishers versus defectors, with implications for understanding crime dynamics.

Contribution

It calculates the critical line between norm preservation and breakdown in a social contagion model, emphasizing the impact of persistent punishers on social stability.

Findings

The critical line depends more on always-punish agents than always-defect agents.

The model relates to crime data in European countries around 1990.

The study provides a quantitative framework for norm dynamics on social networks.

Abstract

The norm game (NG) introduced by Robert Axelrod is a convenient frame to disccuss the time evolution of the level of preserving norms in social systems. Recently NG was formulated in terms of a social contagion on a model social network with two stable states: defectors or punishers. Here we calculate the critical line between these states on the plane of parameters, which measure the severities of punishing and of being punished. We show also that the position of this line is more susceptible to the amount of agents who always punish and never defect, than to those who always defect and never punish. The process is discussed in the context of the statistical data on crimes in some European countries close to Wroc{\l}aw - the place of this Conference - around 1990.