Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

F. Fabiani*, Barbara Franci, S. Sagratella, M. Schmidt, Mathias Staudigl

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the agents update through iterations by choosing an exact optimal strategy; ii) the game admits an exact potential and the agents adopt approximated optimal responses. By exploiting the properties of integer-compatible regularization functions used as penalty terms, we show that both algorithms converge to either an exact or an epsilon-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.
Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control (CDC)
Pages4137-4142
Number of pages6
DOIs
Publication statusPublished - 2022
Event2022 IEEE 61st Conference on Decision and Control - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Conference

Conference2022 IEEE 61st Conference on Decision and Control
Abbreviated titleCDC 2022
Country/TerritoryMexico
CityCancun
Period6/12/229/12/22

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