### Abstract

We consider a class a stochastic nonzero-sum games of the mean-field (MF) type where a generic player's loss function is a convex combination of two quadratic terms: The deviation of the player's action variable from a random variable (target) which the player observes in additive noise, and deviation of the action variable from the average of the actions of all the players. Statistics of all the random variables are Gaussian. For this model, we obtain analytic expressions for Nash and MF equilibria, establish uniqueness of both as well as a direct correspondence between the two, obtain precise values of the coefficient of the leading term in the approximation to the Nash equilibrium of the finite-player game as provided by the solution of the MF game, and derive the unique distribution for the MF term which turns out not to be deterministic. We also apply the results to a price model of oligopoly with a large number of firms (players).

Original language | English (US) |
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Title of host publication | 2018 Annual American Control Conference, ACC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6521-6526 |

Number of pages | 6 |

ISBN (Print) | 9781538654286 |

DOIs | |

State | Published - Aug 9 2018 |

Event | 2018 Annual American Control Conference, ACC 2018 - Milwauke, United States Duration: Jun 27 2018 → Jun 29 2018 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2018-June |

ISSN (Print) | 0743-1619 |

### Other

Other | 2018 Annual American Control Conference, ACC 2018 |
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Country | United States |

City | Milwauke |

Period | 6/27/18 → 6/29/18 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*2018 Annual American Control Conference, ACC 2018*(pp. 6521-6526). [8431664] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431664