Risk-Return Relationship in a Complex Adaptive System

For survival and development, autonomous agents in complex adaptive systems involving the human society must compete against or collaborate with others for sharing limited resources or wealth, by using different methods. One method is to invest, in order to obtain payoffs with risk. It is a common belief that investments with a positive risk-return relationship (namely, high risk high return and vice versa) are dominant over those with a negative risk-return relationship (i.e., high risk low return and vice versa) in the human society; the belief has a notable impact on daily investing activities of investors. Here we investigate the risk-return relationship in a model complex adaptive system, in order to study the effect of both market efficiency and closeness that exist in the human society and play an important role in helping to establish traditional finance/economics theories. We conduct a series of computer-aided human experiments, and also perform agent-based simulations and theoretical analysis to confirm the experimental observations and reveal the underlying mechanism. We report that investments with a negative risk-return relationship have dominance over those with a positive risk-return relationship instead in such a complex adaptive systems. We formulate the dynamical process for the system's evolution, which helps to discover the different role of identical and heterogeneous preferences. This work might be valuable not only to complexity science, but also to finance and economics, to management and social science, and to physics.