Evolutionary game theory: the mathematics of evolution and collective behaviours
It addresses theoretical and applied problems in evolutionary dynamics and AI safety for researchers in mathematics and technology policy, but is incremental in extending existing methods.
The paper applies evolutionary game theory to analyze the statistical properties of equilibria in random evolutionary games and to model the evolution of safety behaviors in the context of AI technology races, providing mathematical insights into collective behaviors and risks.
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include i) the analysis of statistical properties of the number of (stable) equilibria in a random evolutionary game, and ii) the modelling of safety behaviours' evolution and the risk posed by advanced Artificial Intelligence technologies in a technology development race. Finally, it includes an outlook and some suggestions for future researchers.