Hopf bifurcation in the informational nudging of boundedly rational decision makers

Two alternatives decision making task has been studied by psychologists for decades. In this paper, we consider the problem from a control theoretical point of view where a boundedly rational decision maker repeatedly responds to a strategic revelation of information. Dynamical properties of our previously proposed model are analyzed, and stability result is improved by connecting to a larger set of parameters. We show that an arbitrary mixed-strategy equilibrium point can be created and stabilized if the chosen equilibrium point itself, together with the decision maker's personality and total budget for information provision, meet certain conditions; otherwise, a limit cycle will appear, featuring the occurrence of a Hopf bifurcation in the system.