@inproceedings{14783b090cbc40dfa03c3b2b9a45af7c,
title = "Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points",
abstract = "The paper studies properties of best-response (BR) dynamics in potential games with continuous action sets. It is known that BR dynamics converge to the set of Nash equilibria (NE) in potential games. The set of NE in potential games is composed of local maximizers and saddle points of the potential function. The paper studies non-convergence of BR dynamics to saddle points of the potential function. Under relatively mild assumptions it is shown that BR dynamics may only converge to an interior saddle-point from a measure-zero set of initial conditions. This provides a weak stable manifold theorem in this context.",
keywords = "Best-response dynamics, Game theory, Learning, Local maximum, Nash equilibrium, Potential game, Saddle point",
author = "Brian Swenson and Ryan Murray and Soummya Kar and Poor, {H. Vincent}",
note = "Funding Information: This work was supported in part by the Air Force Office of Scientific Research under MURI Grant FA9550-18-1-0502 ∗These authors contributed equally. †Department of Electrical Engineering, Princeton University, Princeton, NJ 08540 (bswenson@princeton.edu and poor@princeton.edu), ‡Department of Mathematics, Pennsylvania State University, State College, PA 16802 (rwm22@psu.edu), ★Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 (soummyak@andrew.cmu.edu). 1Unless otherwise stated, when we refer to a potential game, we mean a potential game with continuous action sets.; 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 ; Conference date: 28-10-2018 Through 31-10-2018",
year = "2019",
month = feb,
day = "19",
doi = "10.1109/ACSSC.2018.8645541",
language = "English (US)",
series = "Conference Record - Asilomar Conference on Signals, Systems and Computers",
publisher = "IEEE Computer Society",
pages = "310--315",
editor = "Matthews, {Michael B.}",
booktitle = "Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018",
address = "United States",
}