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Generalized Differential Games

Author

Listed:
  • E. N. Barron

    (Loyola University Chicago)

  • K. T. Nguyen

    (North Carolina State University)

Abstract

An important generalization of a Nash equilibrium is the case when the players must choose strategies which depend on the other players. The case in zero-sum differential games with players y and z when there is a constraint of the form $$g(y,z) \le 0$$ g ( y , z ) ≤ 0 is introduced. The Isaacs’ equations for the upper value and the lower value of a zero-sum differential game are derived and a condition guaranteeing existence of value is derived. It is also proved that the value functions are the limits of penalized games.

Suggested Citation

  • E. N. Barron & K. T. Nguyen, 2023. "Generalized Differential Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 705-720, September.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00452-0
    DOI: 10.1007/s13235-022-00452-0
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    References listed on IDEAS

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    1. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
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