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Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians

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  • Paola Mannucci

Abstract

We study a nonzero-sum stochastic differential game under the assumptions that the control sets are multidimensional convex compact, the game has separate dynamic and running costs and the multifunctions representing the optimal feedbacks have convex values. To prove the existence of Nash equilibria we reduce to study a system of uniformly parabolic equations strongly coupled by multivalued applications. We obtain the existence of Nash points in two different cases: (i) $\mathbb{R}$ -valued process and general dynamic, (ii) multivalued process and affine dynamic. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:3:p:329-344
    DOI: 10.1007/s13235-013-0101-z
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    References listed on IDEAS

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    1. Pierre Cardaliaguet & Slawomir Plaskacz, 2003. "Existence and uniqueness of a Nash equilibrium feedback for a simple nonzero-sum differential game," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 33-71, December.
    2. A. Bensoussan & J. Frehse, 2000. "Stochastic Games for N Players," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 543-565, June.
    3. 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.
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    Cited by:

    1. Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.

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