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Differential games without pure strategy saddle-point solutions

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Abstract

In some two-player, zero-sum differential games, pure strategy saddle-point solutions do not exist. For such games, the concept of a minmax strategy is examined, and sufficient conditions for a control to be a minmax control are presented. Both the open-loop and the closed-loop cases are considered.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois

    W. E. Schmitendorf (Associate Professor)

Authors
  1. W. E. Schmitendorf
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Additional information

Communicated by Y. C. Ho

The research was partially supported by ONR under Contract No. N00014-69-A-0200-12. An earlier version of this paper was presented at the Eleventh Annual Allerton Conference on Circuit and System Theory, Monticello, Illinois, 1973.

The author wishes to acknowledge his many valuable discussions of this problem with Professor G. Leitmann and also to thank one of the reviewers for his suggestions for simplifying the proof of Theorem 2.1.

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Schmitendorf, W.E. Differential games without pure strategy saddle-point solutions. J Optim Theory Appl 18, 81–92 (1976). https://doi.org/10.1007/BF00933796

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