Journal of Optimization Theory and Applications

, Volume 18, Issue 1, pp 141–151 | Cite as

On saddle-point optimality in differential games

  • H. L. Stalford
  • G. Leitmann
Contributed Papers
  • 56 Downloads

Abstract

A family of two-person, zero-sum differential games in which the admissible strategies are Borel measurable is defined, and two types of saddle-point conditions are introduced as optimality criteria. In one, saddle-point candidates are compared at each point of the state space with all playable pairs at that point; and, in the other, they are compared only with strategy pairs playable on the entire state space. As a theorem, these two types of optimality are shown to be equivalent for the defined family of games. Also, it is shown that a certain closure property is sufficient for this equivalence. A game having admissible strategies everywhere constant, in which the two types of saddle-point candidates are not equivalent, is discussed.

Key Words

Differential games playability saddle-point optimality 

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References

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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • H. L. Stalford
    • 1
  • G. Leitmann
    • 2
  1. 1.Radar DivisionNaval Research LaboratoryWashington, DC
  2. 2.University of CaliforniaBerkeley

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