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.
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Aumann RJ, Maschler MB (1995) Repeated games with incomplete information. MIT Press, Cambrige, MA
Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. System and control: foundation and applications. Birkhauser, Boston
Cardaliaguet P (2007) Differential games with asymmetric information. SIAM J Control Optim 46(3): 816–838
Cardaliaguet P (2008) Representations formulas for some differential games with asymetric information. J Optim Theory Appl 138(1): 1–16
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
Cardaliaguet P, Rainer C (2009) Stochastic differential games with asymmetric information. Appl Math Optim 59(1): 1–36
Laraki R (2001) Variational inequalities, system of functional equations, and incomplete information repeated games. SIAM J Control Optim 40(2): 516–524
Laraki R (2002) Repeated games with lack of information on one side: the dual differential approach. Math Oper Res 27(2): 419–440
Laraki R (2004) On the regularity of the convexication operator on a compact set. J Convex Anal 11(1): 209–234
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
Rosenberg D, Sorin S (2001) An operator approach to zero-sum repeated games. Israel J Math 21: 221–246
Sorin S (2002) A first course on zero-sum repeated games. Springer, Berlin
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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
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DOI: https://doi.org/10.1007/s00182-009-0217-y