## Abstract

Generalized Nash equilibrium problems describe multi-agent systems where each decision maker, or agent, aims at minimizing its individual cost function, yet all are subject to shared, coupling constraints. Distributed algorithms represent viable solution methods for solving generalized Nash equilibrium problems, since they require the agents to optimize and communicate locally, besides agree on the shared resources with selected other agents. The design of efficient solution algorithms is however extremely challenging from a theoretical perspective. In this chapter, we show that operator theory offers the appropriate mathematical tools to design distributed solution methods for generalized Nash equilibrium problems.

Original language | English |
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Title of host publication | Analytics for the Sharing Economy |

Subtitle of host publication | Mathematics, Engineering and Business Perspectives |

Editors | Emanuele Crisostom, Bissan Ghaddar, Florian Häusler, Joe Naoum-Sawaya, Giovanni Russo |

Place of Publication | Cham, Switzerland |

Publisher | Springer |

Pages | 39-49 |

ISBN (Electronic) | 978-3-030-35032-1 |

ISBN (Print) | 978-3-030-35031-4 |

DOIs | |

Publication status | Published - 2020 |

## Keywords

- Control Theory
- Generalized nash equilibrium problem
- Monotone operator theory
- Operator splitting