Nash Equilibrium Seeking with Non-doubly Stochastic Communication Weight Matrix

• Main Authors: Farzad Salehisadaghiani, Lacra Pavel
• Format: Article
• Language: English
• Published: European Alliance for Innovation (EAI) 2020-06-01
• Series: EAI Endorsed Transactions on Collaborative Computing
• Subjects: nash equilibrium; communication graph; information exchange
• Online Access: https://eudl.eu/pdf/10.4108/eai.13-7-2018.158526

We propose a distributed Nash equilibrium seeking algorithm in a networked game, where each player has incomplete information on other players’ actions. Players keep estimates and communicate over a strongly connected digraph with their neighbours according to a gossip communication protocol. Due to the asymmetric information exchange between players, a non-doubly (row)-stochastic weight matrix is defined. We prove almost-sure convergence of the algorithm to a Nash equilibrium under diminishing step-sizes. We extend the algorithm to graphical games in which players’ cost functions are dependent only on their neighbouring players in an interference digraph. Given the interference digraph, a communication digraph is designed so that players exchange only their required information. The communication digraph is a subset of the interference digraph and a superset of its transitive reduction. Finally, we verify the efficacy of the algorithm via simulation on a social media behavioural case.