### Abstract

In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. The first is an iterative Tikhonov regularization scheme while the second is an analogously constructed iterative proximal-point method. Both schemes are characterized by the property that the regularization/centering parameter are updated after every iteration, rather than when one has an approximate solution to the regularized problem. Finally, a modified form of the proximal-point scheme is also presented where the weight on the proximal term is updated as well.

Original language | English (US) |
---|---|

Title of host publication | 2010 49th IEEE Conference on Decision and Control, CDC 2010 |

Pages | 1963-1968 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States Duration: Dec 15 2010 → Dec 17 2010 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|

ISSN (Print) | 0191-2216 |

### Other

Other | 2010 49th IEEE Conference on Decision and Control, CDC 2010 |
---|---|

Country | United States |

City | Atlanta, GA |

Period | 12/15/10 → 12/17/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*2010 49th IEEE Conference on Decision and Control, CDC 2010*(pp. 1963-1968). [5717545] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717545

}

*2010 49th IEEE Conference on Decision and Control, CDC 2010.*, 5717545, Proceedings of the IEEE Conference on Decision and Control, pp. 1963-1968, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717545

**Distributed iterative regularization algorithms for monotone Nash games.** / Kannan, Aswin; Shanbhag, Uday V.

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

TY - GEN

T1 - Distributed iterative regularization algorithms for monotone Nash games

AU - Kannan, Aswin

AU - Shanbhag, Uday V.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. The first is an iterative Tikhonov regularization scheme while the second is an analogously constructed iterative proximal-point method. Both schemes are characterized by the property that the regularization/centering parameter are updated after every iteration, rather than when one has an approximate solution to the regularized problem. Finally, a modified form of the proximal-point scheme is also presented where the weight on the proximal term is updated as well.

AB - In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. The first is an iterative Tikhonov regularization scheme while the second is an analogously constructed iterative proximal-point method. Both schemes are characterized by the property that the regularization/centering parameter are updated after every iteration, rather than when one has an approximate solution to the regularized problem. Finally, a modified form of the proximal-point scheme is also presented where the weight on the proximal term is updated as well.

UR - http://www.scopus.com/inward/record.url?scp=79953131958&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953131958&partnerID=8YFLogxK

U2 - 10.1109/CDC.2010.5717545

DO - 10.1109/CDC.2010.5717545

M3 - Conference contribution

AN - SCOPUS:79953131958

SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1963

EP - 1968

BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

ER -