Intermediate flexibility in cooperation games prevents free riding, polarization, and societal disintegration

We explored the properties of a computational model, “APEM,” inspired by empirical work on human group behavior in a coordination game called “The Slider Game.” Players in a network manipulate sliders on computer screens in an effort to achieve across-the-board aggregation on the same side of the slider. The model is an agent-based dynamical system. We studied the model’s behavior under manipulation of a control parameter called “flexibility,” which determines the willingness of players to adjust their behavior as a function of their agreement with their neighbors. Optimal coordination occurs only in a narrow range near the middle of the parameter space (a “Principle of Intermediacy”). Additionally, the model exhibits two types of non-successful asymptotic states, called “fraught” and “obdurate,” as well as a condition of prohibitively slow convergence where its behavior is very noisy. A review of the anthropological literature provides evidence that each regime of failure is a simple version of an empirically observed condition of flummoxed coordination in human societies: polarization, free-riding, and infrastructure disintegration under societal demise, respectively. Although each of these phenomena has been individually studied at some length, we are aware of no prior integrative treatment.