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A Penalty Method Approach for Open-Loop Variational Games with Equality Constraints

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Book cover Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 12))

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Abstract

In this paper we consider the possibility of solving a variational game with equality constraints by using a penalty method approach. Under the assumption that the unconstrained penalized games have open loop Nash equilibria we give conditions on our model to ensure that there exists a subsequence of penalty parameters converging to infinity for which the corresponding sequence of solutions to the penalized games converges to an open loop Nash equilibrium of the constrained game. Our conditions are based on classical growth and convexity conditions found in the calculus of variations. We conclude our paper with some remarks on obtaining the solutions of the penalized games via Leitmann’s direct method.

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References

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Acknowledgements

The authors would like to dedicate this paper to the memory of our friend and colleague Thomas L. Vincent. Additionally, the first author would like to offer his best wishes to his friend and co-author George Leitmann on the occasion of his eighty-fifth birthday.

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Authors and Affiliations

  1. American Mathematical Society, Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI, 48103, USA

    Dean A. Carlson

  2. Graduate School, University of California at Berkeley, Berkeley, CA, 94720, USA

    George Leitmann

Authors
  1. Dean A. Carlson
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  2. George Leitmann
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Correspondence to Dean A. Carlson .

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Editors and Affiliations

  1. , CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Pierre Cardaliaguet

  2. Wilfrid Laurier University, University Ave W 75, Waterloo, N2L 3C5, Ontario, Canada

    Ross Cressman

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Carlson, D.A., Leitmann, G. (2013). A Penalty Method Approach for Open-Loop Variational Games with Equality Constraints. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_8

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