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A Short State of the Art on Multi-Leader-Follower Games

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Bilevel Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 161))

Abstract

Multi-Leader-Follower games are complex optimization problems that mix a bilevel structure with one or more Nash games. Such kinds of models have been already described in the seminal book of H. von Stackelberg ((1934)Marktform und Gleichgewicht. Springer, Berlin); von Stackelberg et al. ((2011) Market structure and equilibrium. Springer, Heidelberg) and are known to perfectly fit to a lot of applications involving non cooperative situations with hierarchical interactions. Nevertheless it is only recently that theoretical and numerical developments for Multi-Leader-Follower problems have been made. This chapter aims to propose a state of the art of this field of research at the frontier between optimization and economics.

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Notes

  1. 1.

    Equilibrium Problem with Complementarity Constraints

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Acknowledgements

This research benefited from the support of the FMJH Program Gaspard Monge in optimization and operation research, and from the support to this program from EDF. The second author was also benefited by a CONICYT grant CONICYT-PFCHA/Doctorado Nacional/2018 N21180645

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Authors and Affiliations

  1. Université de Perpignan, Perpignan, France

    Didier Aussel & Anton Svensson

  2. Universidad de Chile, Santiago, Chile

    Anton Svensson

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  1. Didier Aussel
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Correspondence to Didier Aussel .

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Editors and Affiliations

  1. Institute of Numerical Mathematics and Optimization, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

  2. School of Mathematical Sciences, University of Southampton, Southampton, UK

    Alain Zemkoho

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Aussel, D., Svensson, A. (2020). A Short State of the Art on Multi-Leader-Follower Games. In: Dempe, S., Zemkoho, A. (eds) Bilevel Optimization. Springer Optimization and Its Applications, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-52119-6_3

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