Nash equilibrium seeking for games with non-quadratic payoffs

Paul Frihauf, Miroslav Krstic, Tamer Başar

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


We introduce a non-model based approach for asymptotic, locally stable attainment of Nash equilibria in static noncooperative games with N players. In classical game theory algorithms, each player employs the knowledge of both the functional form of its payoff and the other players' actions. The proposed algorithm, in which the players only measure their own payoff values, is based on the so-called "extremum seeking" approach, which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient. We consider static games where the players seek to maximize their non-quadratic payoff functions. Since non-quadratic payoffs create the possibility of multiple, isolated Nash equilibria, our convergence results are local. Specifically, the attainment of any particular Nash equilibrium is not assured for all initial conditions, but only for initial conditions in a set around that specific stable Nash equilibrium. For non-quadratic payoffs, the convergence to a Nash equilibrium is not perfect, but is biased in proportion to the perturbation amplitudes and the third derivatives of the payoff functions. We quantify the size of these residual biases.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781424477456
StatePublished - 2010
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States

ASJC Scopus subject areas

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


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