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N-person differential games governed by infinite-dimensional systems

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Abstract

This paper discussesN-person differential games governed by infinite-dimensional systems. The minimax principle, which is a necessary condition for the existence of open-loop equilibrium strategies, is proved. For linear-quadraticN-person differential games, global necessary and sufficient conditions for the existence of open-loop and closed-loop equilibrium strategies are derived.

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Additional information

This work was supported by the Science Fund of the Chinese Academy of Sciences and the Research Foundation of Purdue University.

The problems discussed in this paper were proposed by Professor G. Chen, during the author's visit to Pensylvania State University, and were completed at Purdue University. The author would like to thank Professors L. D. Berkovitz and G. Chen for their hospitality.

Communicated by L. D. Berkovitz

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Li, X.J. N-person differential games governed by infinite-dimensional systems. J Optim Theory Appl 50, 431–450 (1986). https://doi.org/10.1007/BF00938630

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Key Words

  • Equilibrium strategies
  • infinite-dimensional systems
  • N-person differential games
  • minimax principle
  • linear-quadraticN-person differential games