Distributed Discrete-time Nash Equilibrium Seeking with Markovian Switching Topologies
- Resource Type
- Conference
- Authors
- Fang, Xiao; Wen, Guanghui; Zhang, Kaijie; Ye, Maojiao
- Source
- 2019 IEEE Symposium Series on Computational Intelligence (SSCI) Computational Intelligence (SSCI), 2019 IEEE Symposium Series on. :1988-1993 Dec, 2019
- Subject
- Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
Robotics and Control Systems
Signal Processing and Analysis
Nash equilibrium
Switches
Games
Topology
Cost function
Symmetric matrices
Estimation
Nash euilibrium
game
Markovian switching topology
discrete-time system
- Language
This paper develops a distributed discrete-time algorithm to seek Nash equilibrium for games under Markovian switching topologies. In the game problem considered in this paper, all players are assumed to use gradient-like descent method to update their own actions based on the estimation of all the other players’ actions with the intention to minimize their cost functions. All players exchange their estimation information with their neighbors at each discrete time instant through some undirected graphs that are Markovian switching. Suppose that the transition probability matrix is specified and the union of all switching topologies is connected, it is shown that the players’ actions can converge to the unique Nash equilibrium in the mean square sense for any initial condition. The convergence result is established by utilizing Lyapunov stability theory for discrete-time stochastic systems.