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Semi-cooperative strategies for differential games

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  • Alberto Bressan
  • Wen Shen

Abstract

The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative “semi-cooperative” pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. Copyright Springer-Verlag 2004

Suggested Citation

  • Alberto Bressan & Wen Shen, 2004. "Semi-cooperative strategies for differential games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 561-593, August.
    • Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:561-593
    DOI: 10.1007/s001820400180
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    Cited by:

    1. Paola Mannucci, 2014. "Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians," Dynamic Games and Applications, Springer, vol. 4(3), pages 329-344, September.
    2. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    3. João Ricardo Faria & Peter F. Wanke & João J. Ferreira & Franklin G. Mixon, 2018. "Research and innovation in higher education: empirical evidence from research and patenting in Brazil," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(1), pages 487-504, July.
    4. Alberto Bressan & Deling Wei, 2013. "Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data," Dynamic Games and Applications, Springer, vol. 3(3), pages 341-358, September.
    5. Alberto Bressan & Khai T. Nguyen, 2018. "Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 42-78, March.

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