Pseudo-Gradient Dynamics with Cognitive Predictions in Noncooperative Dynamical Systems

A framework of pseudo-gradient-based noncooperative systems with Level-k thinking under bounded depth of reasoning is proposed. In the characterized framework, each agent believes that he/she is the most sophisticated person in the noncooperative system and is allowed to base their decisions on the predictions about the likely actions of other agents. Depending on a knowledge network of payoff functions, the agents may be able to reasoning the other agents' best-response states and use these predicted states in the pseudogradient dynamics. Some sufficient conditions are presented to guarantee stability of a Nash equilibrium with uncertain sensitivity parameters or uncertain knowledge network of payoff functions. We present a numerical example to illustrate the efficacy of our approach.