Mathematical model written by ordinary differential equations for hysteresis games

In game theory, the hysteresis effect manifests itself in the fact that small differences in one or more parameters lead two systems to opposite stable equilibrium. The mathematical model (called smooth model) of hysteresis game writing by ordinary differential equations with the great parameter K is studied. Estimations of closeness of output functions for smooth and classical models through the continuity module of continuous input function are received. This error can be controlled by increasing the parameter K to a sufficiently large value. The result was conducted by studying of mathematical model and using programs Mathematica, Matlab or Maple. Experiments were carried out, and the obtained results were summarized and presented through evaluations and graphical interpretation.