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Strategy Learning
Published in Hamidou Tembine, Distributed Strategic Learning for Wireless Engineers, 2018
Theorem 2.2.5.6 ([53]). Under the hypothesis HA0-HA2, the best-response dynamics defined in (2.7) globally converges to some Nash equilibrium of the aggregative game. Moreover, for almost all aggregative games satisfying HA0 − HA2 there is a finite sequence of single-player improvements that ends arbitrarily close to a Nash equilibrium.
Distributed heavy-ball algorithm of Nash equilibrium seeking for aggregative games
Published in Journal of Control and Decision, 2022
The aggregative game is a special game model and applications with aggregative characterisation cover smart-grid (Mohsenian-Rad et al., 2010), communication networks (Fan et al., 2006), charging control of plug-in electric vehicles (Ma et al., 2010, 2015) and flow control of communication networks (Yin et al., 2011), among many others. Generally speaking, each player in an aggregative game has a cost function which depends not only on its own decisions but also on an aggregation of all players, and the goal of each player is to minimise its own cost function. In view of this specific form of the cost function in aggregative games, it is sufficient that each player only needs to estimate the aggregative term rather than all the other players' actions, and this fact gives rise to some tailor-made distributed NE seeking algorithms for aggregative games (Gadjov & Pavel, 2019; Grammatico, 2017; Koshal et al., 2016; Shakarami et al., 2019; Ye & Hu, 2016; Ye et al., 2021; Zhang et al., 2020). More specifically, the algorithms in Gadjov and Pavel (2019), Koshal et al. (2016), and Ye et al. (2021) adopt diminishing step sizes to ensure exact convergence and introduce some tuning parameters shared by all players (Liang et al., 2017a; Zhang et al., 2020). However, the rule of diminishing step sizes renders slow convergence while the commonly shared parameters are global information which are difficult to be known by all players. Other algorithms (Grammatico, 2017; Persis & Grammatico, 2020) exchange information with the aggregative term by utilising a one-to-one communication mechanism; in contrast, our distributed algorithm is carried out based on the information exchange with a central aggregative term. Also, unlike the linear aggregative term considered in Koshal et al. (2016), Persis and Grammatico (2020), Shakarami et al. (2019), Ye and Hu (2016), and Ye et al. (2021), we discuss both linear and nonlinear aggregative information. Furthermore, our algorithm differs other existing results (Persis & Grammatico, 2019; Salehisadaghiani & Pavel, 2016) since the privacy of each player is considered in our distributed NE seeking algorithm.