The Group Control Catastrophe

Abstract

This study elaborates a surprising finding by Heckathorn (1990). His simulation of group-mediated social control models a situation in which an agent outside a group tries to obtain compliance by group members through the administration of sanctions. In general, group compliance increases as the agent's monitoring efficacy increases. The surprising finding is that under certain conditions group compliance collapses to zero for intermediate values of the monitoring efficacy. In this study I show this is part of a catastrophe, a bifurcation into two equilibria for intermediate values of the monitoring efficacy. Whether the group exists at a high-compliance or low-compliance equilibrium depends on the occurrence of simultaneous non-payoff-maximizing cooperation or defection. Cooperation pushes the group to the high-compliance equilibrium; defection knocks it to the low-compliance equilibrium. The catastrophe is robust: it exists for a range of parameter values and for different production functions for the public good (benefits from group compliance).