Geodesic
$Z$-equilibria in many-player stochastic differential games
Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 123-133

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In this paper $N$-person nonzero-sum games are considered. The dynamics is described by Ito stochastic differential equations. The cost-functions are conditional expectations of functionals of Bolza type with respect to the initial situation. The notion of $Z$-equilibrium is introduced in many-player stochastic differential games. Some properties of $Z$-equilibria are analyzed. Sufficient conditions are established guaranteeing the $Z$-equilibrium for the strategies of the players. In a particular case of a linear-quadratic game the $Z$-equilibrium strategies are found in an explicit form.
Classification : 90D15, 91A10, 91A60, 93E05
Keywords: nonzero-sum game; many-player game; stochastic differential equation; linear-quadratic game; Bolza functional; cost-function; strategy 
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     author = {Gaidov, Svatoslav},
     title = {$Z$-equilibria in many-player stochastic differential games},
     journal = {Archivum mathematicum},
     pages = {123--133},
     publisher = {mathdoc},
     volume = {29},
     number = {3-4},
     year = {1993},
     mrnumber = {1263113},
     zbl = {0816.93077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1993__29_3-4_a0/}
}
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Gaidov, Svatoslav. $Z$-equilibria in many-player stochastic differential games. Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 123-133. http://geodesic.mathdoc.fr/item/ARM_1993__29_3-4_a0/