On generalized Nash equilibrium in infinite dimension: the Lagrange multipliers approach

Abstract

In this note we study a class of generalized Nash equilibrium problems and characterize the solutions which have the property that all players share the same Lagrange multipliers. Nash equilibria of this kind were introduced by Rosen in 1965, in finite-dimensional spaces. In order to obtain the same property in infinite dimension, we use very recent developments of a new duality theory. In view of its usefulness in the study of time-dependent or stochastic equilibrium problems, an application in Lebesgue spaces is given.

Keywords:

• Nash equilibria
• variational inequalities
• Lagrange multipliers
• infinite dimension
• duality

AMS Subject Classifications::

• 91A10
• 49J40
• 90C46

Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments.