Human Social Cycling Spectrum

This paper investigates the reality and accuracy of evolutionary game dynamics theory in human game behavior experiments. In classical game theory, the central concept is Nash equilibrium, which reality and accuracy has been well known since the firstly illustration by the O'Neill game experiment in 1987. In game dynamics theory, the central approach is dynamics equations, however, its reality and accuracy is rare known, especially in high dimensional games. By develop a new approach, namely the eigencycle approach, with the eigenvectors from the game dynamics equations, we discover the fine structure of the cycles in the same experiments. We show that, the eigencycle approach can increase the accuracy by an order of magnitude in the human dynamic hehavior data. As the eigenvector is fundamental in dynamical systems theory which has applications in natural, social, and virtual worlds, the power of the eigencycles is expectedly. Inspired by the high dimensional eigencycles, we suggest that, the mathematical concept, namely 'invariant manifolds', could be a candidate as the central concept for the game dynamics theory, like the fixed point concept for classical game theory.