Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games

Matthew Zyskowski, Quanyan Zhu

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

Abstract

This paper introduces the Variance of Anarchy (VoA) metric to compliment existing measures of efficiency loss in dynamic games due to decentralized mechanisms. The VoA is inspired by Price of Anarchy (PoA) and Price of Information (PoI) measures that have been used previously in the literature. We propose a new design procedure for decentralized control algorithms using PoA and VoA that identifies the optimal control solution for competing agents among a family of decentralized controllers by solving an optimization of a summed PoA and VoA objective function over a parameter space. The design method is illustrated with a stochastic model for queue server dynamics and two separate optimal control problems - The first involving noncooperative agents, and the second a team. For each problem, a family of density-shaping cumulant controls is computed corresponding to a parametric target cumulant set, and the optimal chosen via this new procedure. Simulation results are provided to compare the controller to a baseline 2CC control.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1720-1725
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

Fingerprint

Stochastic Differential Games
Price of Anarchy
Cumulants
Costs
Decentralized
Measures of Information
Controller
Controllers
Dynamic Games
Decentralized control
Decentralized Control
Stochastic models
Control Algorithm
Design Method
Stochastic Model
Queue
Parameter Space
Optimal Control Problem
Baseline
Optimal Control

Keywords

  • Cost cumulant control
  • Cost density-shaping games
  • Price of anarchy
  • Stochastic differential games
  • Team optimization
  • Telecommunications
  • Variance of anarchy

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Zyskowski, M., & Zhu, Q. (2013). Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 1720-1725). [6760130] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760130

Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games. / Zyskowski, Matthew; Zhu, Quanyan.

2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1720-1725 6760130.

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

Zyskowski, M & Zhu, Q 2013, Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games. in 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013., 6760130, Institute of Electrical and Electronics Engineers Inc., pp. 1720-1725, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760130
Zyskowski M, Zhu Q. Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc. 2013. p. 1720-1725. 6760130 https://doi.org/10.1109/CDC.2013.6760130
Zyskowski, Matthew ; Zhu, Quanyan. / Price and Variance of Anarchy in mean-variance cost density-shaping stochastic differential games. 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. pp. 1720-1725
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