Semi-cooperative strategies for differential games

International Journal of Game Theory

Volumn 32, Issue 4, 2004, Pages 561-593

  Bressan, Alberto ^a,b   Shen, Wen ^a,b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b SISSA   (Italy)

Author keywords

Ill posedness of elliptic Cauchy problems; Pareto optimum; Semi cooperation; Weak hyperbolicity

Indexed keywords

EID: 4344609748     PISSN: 00207276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001820400180     Document Type: Article

References (24)

1. [A] Aubin JP (1979) Mathematical Methods of Game and Economic Theory, North Holland
2. [BC] Bardi M, Capuzzo Dolcetta I (1997) Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser
3. d Edition, Academic Press, London
4. [BB] Bianchini S, Bressan A Vanishing viscosity solutions of nonlinear hyperbolic systems, Annals of Mathematics, to appear.
5. [BS] Bressan A, Shen W Small BV solution of hyperbolic non-cooperative differential games, SIAM J. Control Optim., to appear.
6. [CP] Cardaliaguet P, Plaskacz S (2003) Existence and uniqueness of a Nash equilibrium feedback for a simple non-zero-sum differential game. Int. J. Game Theory 32:33-71
7. [FL] Frid H, Liu IS (1995) Oscillation waves in Riemann problems inside elliptic regions for conservation laws of mixed type, Z. Angew. Math. Phys. 46:913-931
8. [F1] Friedman A (1971) Differential Games, Wiley-Interscience
9. [F2] Friedman A (1972) Stochastic Differential Games, J. Differential Equal. 11:79-108
10. [He] Henry D (1981) Geometric theory of Semilinear Parabolic Equations, Springer Lecture Notes in Math. 840:
11. [HS] Hirsch MW, Smale S, 1974 Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York.
12. [KY] Kreiss HO, Yström J (2002) Parabolic problems which are ill-posed in the zero dissipation limit, Math. Comput. Modeling 35:1271-1295
13. [Lx] Lax P. (1957) Asymptotic solution of oscillatory initial value problems Duke Math. J. 24:627-646
14. [L] Liu TP (1981) Admissible solutions of hyperbolic conservation laws, Amer. Math. Soc. Memoir 240:
15. [Mn] Mannucci P Nonzero sum stochastic differential games with dicontinuous feedback, SIAM J. Control Optim., to appear.
16. [Na] Nash J (1951) Non-cooperative games, Ann. of Math. 2:286-295
17. [OZ1] Oh M, Zumbrun K (2003) Stability of periodic solutions of conservation laws with viscosity: Analysis of the Evans function, Arch. Rational Mech. Anal. 166:99-166
18. [OZ2] Oh M, Zumbrun K (2003) Stability of periodic solutions of conservation laws with viscosity: Pointwise bounds on the Green function, Arch. Rational Mech. Anal. 166:167-196
19. [O] Olsder GJ (2001) On open-and closed-loop bang-bang control in nonzero-sum differential games, SIAM J. of Control Optim. 40:1087-1106
20. [P] Perko L (1991) Differential Equations and Dynamical Systems, Springer-Verlag
21. [S1] Serre D (2000) Systems of Conservation Laws I, II. Cambridge University Press
22. [S2] Serre D The stability of periodic solutions of viscous conservation laws: Large wavelength perturbations, Preprint
23. [Sm] Smale S (2000) The prisoner's dilemma and dynamical systems associated to non-cooperative games, In: Cucker F, Wong R (eds.), The Collected Papers of Stephen Smale, World Scientific
24. [VZ] Vaisbord EM, Zhukovskii VI (1988) Introduction to Multi-players Differential Games and their Applications, Gordon and Breach Science Publishers