Rationality Levels in a Heterogeneous Dynamic Price Game

The Bertrand game is one of the basic game models in modern microeconomics. In some behavior experiments with game theory, it was shown that agents have different bounded rationality levels. In order to check the effect of bounded rationality levels on the stability of the equilibrium points in Bertrand games, this study establishes a new dynamic price game with a parameter to show the rationality levels. An exact geometrical characterization of the stable region of the dynamic system is firstly proposed, from which the critical points of the bifurcation of the system can be deduced. It is shown that allowing various bounded rationalities is conducive to enlarging the stable region of the equilibrium point of the price system. With increasing rationality level, the stable region expands. Numerical examples are provided to show the main results.