Existence of Nash Equilibria on Integer Programming Games

  • Margarida Carvalho
  • Andrea Lodi
  • João Pedro Pedroso
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)

Abstract

We aim to investigate a new class of games, where each player’s set of strategies is a union of polyhedra. These are called integer programming games. To motivate our work, we describe some practical examples suitable to be modeled under this paradigm. We analyze the problem of determining whether or not a Nash equilibria exists for an integer programming game, and demonstrate that it is complete for the second level of the polynomial hierarchy.

Keywords

Integer programming games Nash equilibria Computational complexity 

Notes

Acknowledgements

Part of this work was performed while the first author was in the Faculty of Sciences University of Porto and INESC TEC. The first author thanks the support of Institute for data valorisation (IVADO), the Portuguese Foundation for Science and Technology (FCT) through a PhD grant number SFRH/BD/79201/2011 and the ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, and National Funds through the FCT (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013. We thank the referees for comments and questions that helped clarifying the presentation.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Margarida Carvalho
    • 1
  • Andrea Lodi
    • 2
  • João Pedro Pedroso
    • 3
  1. 1.IVADO FellowCanada Excellence Research Chair, École Polytechnique de MontréalMontrealCanada
  2. 2.Canada Excellence Research ChairÉcole Polytechnique de MontréalMontrealCanada
  3. 3.Faculdade de Ciências Universidade do Porto and INESC TECPortoPortugal

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