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Equilibria of Parametrized N-Player Nonlinear Games Using Inequalities and Nonsmooth Dynamics

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Computational Mathematics and Variational Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 159))

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Abstract

In this paper we present a combination of theoretical and computational results meant to give insights into the question of existence of non-unique Nash equilibria for N-players nonlinear games. Our inquiries make use of the theory of variational inequalities and projected systems to highlight cases where multiplayer Nash games with parametrized payoffs exhibit changes in the number of Nash equilibria, depending on given parameter values.

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Notes

  1. 1.

    We consider the reader is familiar with the definitions of tangent and normal cones to a closed, convex subset of the Euclidean space at a given point in the set (see [9])

  2. 2.

    Let H be a Hilbert space and K a closed and convex subset in H. A mappingF : K → X is called continuous on finite dimensional subspaces if for any finite dimensional subspace S ⊂ H, the restriction of F to K ∩ S is weakly continuous.

  3. 3.

    This stage is very important to our approach and is different than other algorithmic solutions for VI problems, as we implement a projection type method to trace trajectories of the PDS which end up in local monotone attractors.

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Acknowledgements

This work has been supported by a National Science and Engineering Research Council (NSERC) Discovery Grant 400684 of the first author.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada

    Monica G. Cojocaru & Fatima Etbaigha

Authors
  1. Monica G. Cojocaru
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  2. Fatima Etbaigha
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Corresponding author

Correspondence to Monica G. Cojocaru .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Cojocaru, M.G., Etbaigha, F. (2020). Equilibria of Parametrized N-Player Nonlinear Games Using Inequalities and Nonsmooth Dynamics. In: Daras, N., Rassias, T. (eds) Computational Mathematics and Variational Analysis. Springer Optimization and Its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-030-44625-3_3

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