On the characterization of solution sets of smooth and nonsmooth stochastic nash games

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Abstract

Variational analysis provides an avenue for characterizing solution sets of deterministic Nash games over continuous strategy sets. We examine whether similar statements, particularly pertaining to existence and uniqueness may be made, when player objectives are given by expectations of either smooth or nonsmooth functions. In general, a direct application of deterministic results is difficult since the expectation operation results in a less tractable nonlinear function. Our interest is in developing an analytical framework that only requires the analysis of the integrands of the expectations. Accordingly, in both the smooth and nonsmooth settings, we show that if an appropriate coercivity result holds in an almost-sure fashion, then the existence of an equilibrium to the original stochastic Nash game may be claimed. In the smooth setting, a corresponding sufficiency condition for uniqueness is also provided. We illustrate the utility of our framework by examining a class of stochastic Nash-Cournot games in which nonsmoothness arises from the use of a risk measure.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages5632-5637
Number of pages6
StatePublished - Oct 15 2010
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

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All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Ravat, U., & Shanbhag, V. V. (2010). On the characterization of solution sets of smooth and nonsmooth stochastic nash games. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 5632-5637). [5531036]