Two-Level Incentive Stackelberg Strategies in LQ Differential Games with Two Noncooperative Leaders and One Follower

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  • MIZUKAMI Koichi
    Faculty of Integrated Arts and Sciences, Hiroshima University
  • Wu Hansheng
    Faculty of Integrated Arts and Sciences, Hiroshima University

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  • Two Level Incentive Stackelberg Strateg

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This paper mainly is concerned with the derivation of the sufficient conditions for the two-level incentive stackelberg strategies in the two-level hierarchical differential games with two noncooperative leaders and one follower, characterized by a kind of linear state dynamics and quadratic cost functionals. In the present paper, we first define a concept of “team-optimal Nash equilibrium solution”, and by a simple numerical example, show a general method solving such a static two-level incentive game in which two leaders find their “team-optimal Nash equilibrium solution” by announcing their strategies. Then, we construct the two-level incentive Stackelberg strategies γ1∈Γ1 and γ2∈Γ2 of the formγ1(x(t), u31(t), t)=η10(t)x(t)+η11(t)u31(t), γ2(x(t), u32(t), t)=η20(t)x(t)+η22(t)u32(t), for the players P1 and P2 (leaders) to achieve their “team-optimal Nash equilibrium solution” in such a game characterized by a kind of linear state dynamics and quadratic cost functionals, and also obtain the sufficient conditions which are satisfied by these two-level incentive Stackelberg strategies γ1∈Γ1 and γ2∈Γ2.

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