Distributed Nash Equilibrium Seeking Algorithms for Two-Layer Constrained Non-Cooperative Games

This paper studies the Nash equilibrium seeking problem for two-layer constrained non-cooperative games. In particular, the non-cooperative game among upper-layer clusters is played by lower-layer players therein subject to set constraints. In each cluster, a player is appointed as an administrator who is responsible for interacting with other clusters. A KKT condition is first determined to formulate the underlying generalized Nash equilibrium. Based on such a KKT condition, a distributed seeking algorithm using a projection operator is proposed. In particular, under the assumption that each player has access to the administrators in other clusters, the proposed seeking algorithm via intra-cluster interaction guarantees that each player is capable of seeking its corresponding component of the generalized Nash equilibrium. An illustrative example effectively verifies the proposed theoretical results.