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N-person Linear - Non- Quadratic Differential Games

Author: WangFei
Tutor: PanLiPing
School: Fudan University
Course: Operational Research and Cybernetics
Keywords: N-person differential games linear-nonquadratic nonzero-sum closed-loop Nash equilibrium strategy closed-loop representation of the open-loop Nash equilibrium strat-egy
CLC: O225
Type: Master's thesis
Year: 2011
Downloads: 27
Quote: 0
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Abstract


This paper studies the nonzero-sum differential game problem consisting of a linear time-variant system driven by N-person and corresponding objective functionals.Two quasi-Riccati equations—(4.1)and(6.1),and a nonlinear integral equations family—(5.1) are given.Taking ad-vantage of the regular solution of (6.1),a closed-loop Nash equilibrium strategy is derived;The closed-loop representation of the open-loop Nash equilibrium strategy is obtained by making use of Pontryagin’s maximum principle and the normal solution of (4.1). Besides,the two-way relationships between the normal solution of (4.1) and the continuously differentiable solutions family of (5.1) are revealed.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Game theory ( game theory )
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