Abstract
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an auxiliary optimization problem over a set of measure-valued processes. Then we use this equivalent formulation to characterize the value function as the viscosity solution of a special type of a Hamilton–Jacobi equation. This paper generalizes the results of a previous work of the authors (Math. Oper. Res. 34(4), 769–794, 2009), where only a finite number of possible payoffs is considered.
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Acknowledgements
This work has been supported by the Commission of the European Communities under the 7th Framework Programme Marie Curie Initial Training Networks Project “Deterministic and Stochastic Controlled Systems and Applications” FP7-PEOPLE-2007-1-1-ITN, No. 213841-2 and the French National Research Agency ANR-10-BLAN 0112.
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Cardaliaguet, P., Rainer, C. Games with Incomplete Information in Continuous Time and for Continuous Types. Dyn Games Appl 2, 206–227 (2012). https://doi.org/10.1007/s13235-012-0043-x
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DOI: https://doi.org/10.1007/s13235-012-0043-x