Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points

Brian Swenson, Ryan William Murray, Soummya Kar, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationConference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages310-315
Number of pages6
ISBN (Electronic)9781538692189
DOIs
StatePublished - Feb 19 2019
Event52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 - Pacific Grove, United States
Duration: Oct 28 2018Oct 31 2018

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2018-October
ISSN (Print)1058-6393

Conference

Conference52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
CountryUnited States
CityPacific Grove
Period10/28/1810/31/18

Fingerprint

Dynamic response

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

Cite this

Swenson, B., Murray, R. W., Kar, S., & Poor, H. V. (2019). Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points. In M. B. Matthews (Ed.), Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 (pp. 310-315). [8645541] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2018.8645541
Swenson, Brian ; Murray, Ryan William ; Kar, Soummya ; Poor, H. Vincent. / Best-Response Dynamics in Continuous Potential Games : Non-Convergence to Saddle Points. Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018. editor / Michael B. Matthews. IEEE Computer Society, 2019. pp. 310-315 (Conference Record - Asilomar Conference on Signals, Systems and Computers).
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Swenson, B, Murray, RW, Kar, S & Poor, HV 2019, Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points. in MB Matthews (ed.), Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018., 8645541, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2018-October, IEEE Computer Society, pp. 310-315, 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018, Pacific Grove, United States, 10/28/18. https://doi.org/10.1109/ACSSC.2018.8645541

Best-Response Dynamics in Continuous Potential Games : Non-Convergence to Saddle Points. / Swenson, Brian; Murray, Ryan William; Kar, Soummya; Poor, H. Vincent.

Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018. ed. / Michael B. Matthews. IEEE Computer Society, 2019. p. 310-315 8645541 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - 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.

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Swenson B, Murray RW, Kar S, Poor HV. Best-Response Dynamics in Continuous Potential Games: Non-Convergence to Saddle Points. In Matthews MB, editor, Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018. IEEE Computer Society. 2019. p. 310-315. 8645541. (Conference Record - Asilomar Conference on Signals, Systems and Computers). https://doi.org/10.1109/ACSSC.2018.8645541