Bang–bang-type Nash equilibrium point for Markovian nonzero-sum stochastic differential game

Said Hamadène; Rui Mu

doi:10.1016/j.crma.2014.06.011

Optimal control/Game theory

Bang–bang-type Nash equilibrium point for Markovian nonzero-sum stochastic differential game

Presented by: the Editorial Board

Said Hamadène ¹; Rui Mu ^1,²

¹ Université du Maine, LMM, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
² School of Mathematics, Shandong University, Jinan 250100, China

Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 699-706.

Abstract
Résumé

In this Note, we solve a nonzero-sum stochastic differential game (NZSDG) with bang–bang-type equilibrium controls by using backward stochastic differential equations (BSDEs). The generator is multi-dimensional and discontinuous with respect to z.

Dans cette Note, nous résolvons un jeu différentiel stochastique de somme non nulle avec contrôles d'équilibre de type bang–bang, en utilisant les équations différentielles stochastiques rétrogrades (EDSRs). Le générateur est multi-dimensionnel et discontinu par rapport à z.

Received: 2014-02-12
Accepted: 2014-06-20
Published online: 2014-07-29

DOI: 10.1016/j.crma.2014.06.011

Author's affiliations:

Said Hamadène ¹; Rui Mu ^{1, 2}

¹ Université du Maine, LMM, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
² School of Mathematics, Shandong University, Jinan 250100, China

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     author = {Said Hamad\`ene and Rui Mu},
     title = {Bang{\textendash}bang-type {Nash} equilibrium point for {Markovian} nonzero-sum stochastic differential game},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {699--706},
     publisher = {Elsevier},
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     language = {en},
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Said Hamadène; Rui Mu. Bang–bang-type Nash equilibrium point for Markovian nonzero-sum stochastic differential game. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 699-706. doi : 10.1016/j.crma.2014.06.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.06.011/

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