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Sufficiency and game structure in Nash open-loop differential games

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Abstract

This note deals with the following problem inN-player Nash open-loop differential games: Which conditions on the Hamiltonians will simplify the verification of the sufficient conditions? In the class of games with Hamiltonians linear in the state, and where the state is separated from the control of playeri in the Hamiltonian of this player, the first-order and second-order conditions for an extremum of the Hamiltonian of playeri also constitute a set of sufficient conditions.

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References

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Authors and Affiliations

  1. Institute of Theoretical Statistics, Copenhagen School of Economics and Business Administration, Copenhagen, Denmark

    S. Jørgensen (Associate Professor)

Authors
  1. S. Jørgensen
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Additional information

Communicated by G. Leitmann

The helpful comments of Professor G. Leitmann are gratefully acknowledged.

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Jørgensen, S. Sufficiency and game structure in Nash open-loop differential games. J Optim Theory Appl 50, 189–193 (1986). https://doi.org/10.1007/BF00938485

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  • DOI: https://doi.org/10.1007/BF00938485

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