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Some partially observed multi-agent linear exponential quadratic stochastic differential games

The author was supported by NSF grant DMS 1411412, AFOSR grant FA9550-17-1-0073, and ARO grant W911NF-14-10390.
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  • Some multi-agent stochastic differential games described by a stochastic linear system driven by a Brownian motion and having an exponential quadratic payoff for the agents are formulated and solved. The agents have either complete observations or partial observations of the system state. The agents act independently of one another and the explicit optimal feedback control strategies form a Nash equilibrium. In the partially observed problem the observations are the same for all agents which occurs in broadcast situations. The optimal control strategies and optimal payoffs are given explicitly. The method of solution for both problems does not require solving either Hamilton-Jacobi-Isaacs equations or backward stochastic differential equations.

    Mathematics Subject Classification: Primary: 91A15, 49N70; Secondary: 91A25.


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