Skip to main content
Log in

Approximation and representation of the value for some differential games with asymmetric information

  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

We consider differential games with incomplete information. For special games with dynamics independent of the state of the system and linear payoffs, we give a representation formula for the value similar to the value of repeated games with lack of information on both sides. For general games, this representation formula does not hold and we introduce an approximation of the value: we build a sequence of functions converging to the value function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aumann RJ, Maschler MB (1995) Repeated games with incomplete information. MIT Press, Cambrige, MA

    Google Scholar 

  • Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. System and control: foundation and applications. Birkhauser, Boston

    Book  Google Scholar 

  • Cardaliaguet P (2007) Differential games with asymmetric information. SIAM J Control Optim 46(3): 816–838

    Article  Google Scholar 

  • Cardaliaguet P (2008) Representations formulas for some differential games with asymetric information. J Optim Theory Appl 138(1): 1–16

    Article  Google Scholar 

  • Cardaliaguet P (2009) Numerical approximation and optimal strategies for differential games with lack of information on one side. “Advances in differential games and their applications - Analytical and numerical developments” Annals of the International Society of Dynamic Games. Birkhäuser, Boston, pp 159–176

  • Cardaliaguet P, Quincampoix M (2008) Deterministic differential games under probability knowledge of initial condition. Int Game Theory Rev 10(1): 1–16

    Article  Google Scholar 

  • Cardaliaguet P, Rainer C (2009) Stochastic differential games with asymmetric information. Appl Math Optim 59(1): 1–36

    Article  Google Scholar 

  • Laraki R (2001) Variational inequalities, system of functional equations, and incomplete information repeated games. SIAM J Control Optim 40(2): 516–524

    Article  Google Scholar 

  • Laraki R (2002) Repeated games with lack of information on one side: the dual differential approach. Math Oper Res 27(2): 419–440

    Article  Google Scholar 

  • Laraki R (2004) On the regularity of the convexication operator on a compact set. J Convex Anal 11(1): 209–234

    Google Scholar 

  • Mertens JF, Zamir S (1971) The value of two person zero sum repeated games with lack of information on both sides. Int J Game Theory 1(1): 39–64

    Article  Google Scholar 

  • Rosenberg D, Sorin S (2001) An operator approach to zero-sum repeated games. Israel J Math 21: 221–246

    Article  Google Scholar 

  • Sorin S (2002) A first course on zero-sum repeated games. Springer, Berlin

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Souquière.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Souquière, A. Approximation and representation of the value for some differential games with asymmetric information. Int J Game Theory 39, 699–722 (2010). https://doi.org/10.1007/s00182-009-0217-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00182-009-0217-y

Keywords

Navigation