Using Nash equilibrium in Machine Learning scenarios part1
Basics of Nash equilibrium
https://www.masterclass.com/articles/nash-equilibrium-explained
- Distributed Nash Equilibrium Seeking with Stochastic Event-Triggered Mechanism(arXiv)
Author : Wei Huo, Kam Fai Elvis Tsang, Yamin Yan, Karl Henrik Johansson, Ling Shi
Abstract : In this paper, we study the problem of consensus-based distributed Nash equilibrium (NE) seeking where a network of players, abstracted as a directed graph, aim to minimize their own local cost functions non-cooperatively. Considering the limited energy of players and constrained bandwidths, we propose a stochastic event-triggered algorithm by triggering each player with a probability depending on certain events, which improves communication efficiency by avoiding continuous communication. We show that the distributed algorithm with the developed event-triggered communication scheme converges to the exact NE exponentially if the underlying communication graph is strongly connected. Moreover, we prove that our proposed event-triggered algorithm is free of Zeno behavior. Finally, numerical simulations for a spectrum access game are provided to illustrate the effectiveness of the proposed mechanism by comparing it with some existing event-triggered methods
2. Linear convergence in time-varying generalized Nash equilibrium problems(arXiv)
Author : Mattia Bianchi, Emilio Benenati, Sergio Grammatico
Abstract : We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.
