Necessary and Sufficient Condition for Two-Player Stackelberg Strategy

This technical note revisits the open-loop Stackelberg strategy for a two-player game. By introducing a new costate, which captures the future information of the control input, we present a necessary and sufficient condition for the existence and uniqueness of the two-player game. The optimal strategy is designed in terms of three decoupled and symmetric Riccati equations which improves the existing results greatly on computation.

[1]  Pierre Bernhard,et al.  Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions , 1979 .

[2]  Conjectural variation based bidding strategy in spot markets: fundamentals and comparison with classical game theoretical bidding strategies , 2003 .

[3]  J. Cruz,et al.  Additional aspects of the Stackelberg strategy in nonzero-sum games , 1973 .

[4]  B. Gardner,et al.  Feedback Stackelberg strategy for M-level hierarchical games , 1978 .

[5]  Hisham Abou-Kandil,et al.  Discrete time Fuggati equations in open loop Nash and Stackelberg games , 1997 .

[6]  Y. Ho,et al.  Nonzero-sum differential games , 1969 .

[7]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[8]  Gerhard Freiling,et al.  Discrete time Fuggati equations in open loop Nash and Stackelberg games , 1997, 1997 European Control Conference (ECC).

[9]  Emmanuel Trélat,et al.  Stackelberg strategy with closed-loop information structure for linear-quadratic games , 2006 .

[10]  Radu Stefan,et al.  General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations , 2009, SIAM J. Matrix Anal. Appl..

[11]  E. Trélat,et al.  Min-max and min-min stackelberg strategies with closed-loop information structure , 2011 .

[12]  Marc Jungers,et al.  On Linear-Quadratic Stackelberg Games With Time Preference Rates , 2008, IEEE Transactions on Automatic Control.

[13]  J. Cruz,et al.  On the Stackelberg strategy in nonzero-sum games , 1973 .

[14]  Marc Jungers,et al.  Matrix block formulation of closed-loop memoryless Stackelberg strategy for discrete-time games , 2008, 2008 47th IEEE Conference on Decision and Control.

[15]  Gerhard Freiling,et al.  Existence and Uniqueness of Open-Loop Stackelberg Equilibria in Linear-Quadratic Differential Games , 2001 .

[16]  G. Leitmann On generalized Stackelberg strategies , 1978 .

[17]  T. Başar,et al.  Stackelberg strategies in linear-quadratic stochastic differential games , 1981 .

[18]  L. Mirkin,et al.  H/sup /spl infin// control and estimation with preview-part II: fixed-size ARE solutions in discrete time , 2005, IEEE Transactions on Automatic Control.

[19]  C. Chen,et al.  Stackelburg solution for two-person games with biased information patterns , 1972 .

[20]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[21]  H. Abou-Kandil,et al.  Necessary conditions for constant solutions of coupled Riccati equations in Nash games , 1993 .

[22]  G. Freiling,et al.  Solvability condition for a nonsymmetric Riccati equation appearing in stackelberg games , 2003, 2003 European Control Conference (ECC).