Nash equilibrium, dynamics and control of congestion games with resource failures

This study investigates a class of congestion games with resource failures (CGRF). Since the CGRF is not necessarily equivalent to a potential game, it is difficult to discuss the existence of Nash equilibrium (NE). To improve this case, a sufficient condition is proposed that CGRF must be a potential game. Then the following studies are all based on the idea that CGRF is a potential game. Firstly, all NEs of CGRF are found with the help of the potential function. Secondly, the dynamic convergence problem of evolutionary CGRF is considered by means of the semi-tensor product of matrices. A necessary and sufficient condition to determine whether the evolutionary CGRF can converge globally to the set of NEs is derived. Furthermore, an event-triggered controller is designed to ensure the global convergence of the evolutionary CGRF. Finally, the effectiveness of the obtained results is verified by an illustrative example.