Stability of Gradient Learning Dynamics in Continuous Games: Scalar Action Spaces

11/07/2020
by   Benjamin J. Chasnov, et al.
0

Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural notion of a local equilibrium is a differential Nash equilibrium. However, the set of locally exponentially stable equilibria of the learning dynamics do not necessarily coincide with the set of differential Nash equilibria of the corresponding game. To characterize this gap, we provide formal guarantees for the stability or instability of such fixed points by leveraging the spectrum of the linearized game dynamics. We provide a comprehensive understanding of scalar games and find that equilibria that are both stable and Nash are robust to variations in learning rates.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/07/2020

Stability of Gradient Learning Dynamics in Continuous Games: Vector Action Spaces

Towards characterizing the optimization landscape of games, this paper a...
06/29/2018

Learning with minimal information in continuous games

We introduce a stochastic learning process called the dampened gradient ...
11/19/2018

Nash equilibrium seeking in potential games with double-integrator agents

In this paper, we show the equivalence between a constrained, multi-agen...
06/24/2022

Diegetic representation of feedback in open games

We improve the framework of open games with agency by showing how the pl...
06/04/2021

Coordination problems on networks revisited: statics and dynamics

Simple binary-state coordination models are widely used to study collect...
05/22/2019

Equilibrium Characterization for Data Acquisition Games

We study a game between two firms in which each provide a service based ...
04/08/2018

Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

Stochastic stability is a popular solution concept for stochastic learni...