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nonzero-sum game; many-player game; stochastic differential equation; linear-quadratic game; Bolza functional; cost-function; strategy
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.
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