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Differential Games of inf-sup Type and Isaacs Equations

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Abstract

Motivated by the work of Fleming, we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and lower bounds for the generators of inf-sup type are upper and lower Hamiltonians, respectively. In particular, the lower (resp. upper) bound corresponds to the progressive (resp. strictly progressive) strategy. By the Dynamic Programming Principle and identification of the generator, we can prove that the inf-sup type game is characterized as the unique viscosity solution of the Isaacs equation. We also discuss the Isaacs equation with a Hamiltonian of a convex combination between the lower and upper Hamiltonians.

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

    Hidehiro Kaise

  2. Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, Republic of China

    Shuenn-Jyi Sheu

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  1. Hidehiro Kaise
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  2. Shuenn-Jyi Sheu
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Correspondence to Hidehiro Kaise or Shuenn-Jyi Sheu.

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Kaise, H., Sheu, SJ. Differential Games of inf-sup Type and Isaacs Equations. Appl Math Optim 52, 1–22 (2005). https://doi.org/10.1007/s00245-004-0818-6

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  • DOI: https://doi.org/10.1007/s00245-004-0818-6

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