New non-equilibrium cobweb dynamical evolution model and its application
A new cobweb model is built under price adjustment situation. Its price correction function considers the dynamic effects of regulation. Accuracy and authenticity of the analysis are increases. The new model is applied to the analysis of stability of power's supply and demand. An empirical analysis is carried out to study electricity power market in Jiangsu province and Shandong province in China. Results from the new model are not identical with the old one. The new model performs better in showing the dynamic effects with price changes and the dynamic law system. Furthermore, the stability for the new cobweb model without considering external influences is also considered. The study shows the stability of new model by numerical analysis. Probability of stability is given.
We prove existence of solutions for a class of systems of subelliptic PDEs arising from Mean Field Game systems with H\"ormander diffusion. These results are motivated by the feedback synthesis Mean Field Game solutions and the Nash equilibria of a large class of $N$-player differential games.