Learning equilibria in constrained Nash-Cournot games with misspecified demand functions

Hao Jiang, Uday V. Shanbhag, Sean P. Meyn

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

4 Scopus citations

Abstract

We consider a constrained Nash-Cournot oligopoly where the demand function is linear. While cost functions and capacities are public information, firms only have partial information regarding the demand function. Specifically, firms either know the intercept or the slope of the demand function and cannot observe aggregate output. We consider a learning process in which firms update their profit-maximizing quantities and their beliefs regarding the unknown demand function parameters, based on disparities between observed and estimated prices. A characterization of the mappings, corresponding to the fixed point of the learning process, is provided. This result paves the way for developing a Tikhonov regularization scheme that is shown to learn the correct equilibrium, in spite of the multiplicity of equilibria. Despite the absence of monotonicity of the gradient maps, we prove the convergence of constant and diminishing steplength distributed gradient schemes under a suitable caveat on the starting points. Notably, precise rate of convergence estimates are provided for the constant steplength schemes.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages1018-1023
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

All Science Journal Classification (ASJC) codes

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

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