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Existence of Projected Solutions for Generalized Nash Equilibrium Problems

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Abstract

We study the existence of projected solutions for generalized Nash equilibrium problems defined in Banach spaces, under mild convexity assumptions for each loss function and without lower semicontinuity assumptions on the constraint maps. Our approach is based on Himmelberg’s fixed point theorem. As a consequence, we also obtain existence of projected solutions for quasi-equilibrium problems and quasi-variational inequalities. Finally, we show the existence of projected solutions for Single-Leader–Multi-Follower games.

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Acknowledgements

We would like to thank the anonymous referees for their valuable remarks and suggestions which certainly improved this work.

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  1. Universidad del Pacífico, Lima, Peru

    Orestes Bueno & John Cotrina

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  1. Orestes Bueno
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  2. John Cotrina
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Correspondence to John Cotrina.

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Communicated by Jafar Zafarani.

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Bueno, O., Cotrina, J. Existence of Projected Solutions for Generalized Nash Equilibrium Problems. J Optim Theory Appl 191, 344–362 (2021). https://doi.org/10.1007/s10957-021-01941-9

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