### 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 |

Volume | 2018-June |

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 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

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

**A Consensus Problem in Mean Field Setting with Noisy Measurements of Target.** / Basar, M Tamer.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2018 Annual American Control Conference, ACC 2018.*vol. 2018-June, 8431664, Institute of Electrical and Electronics Engineers Inc., pp. 6521-6526, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431664

}

TY - GEN

T1 - A Consensus Problem in Mean Field Setting with Noisy Measurements of Target

AU - Basar, M Tamer

PY - 2018/8/9

Y1 - 2018/8/9

N2 - 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).

AB - 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).

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U2 - 10.23919/ACC.2018.8431664

DO - 10.23919/ACC.2018.8431664

M3 - Conference contribution

AN - SCOPUS:85052605345

SN - 9781538654286

VL - 2018-June

SP - 6521

EP - 6526

BT - 2018 Annual American Control Conference, ACC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -