Abstract
Using the duality techniques introduced by De Meyer (Math Oper Res 21:209–236, 1996a, Math Oper Res 21:237–251, 1996b), Rosenberg (Int J Game Theory 27:577–597, 1998) and De Meyer and Marino (Cahiers de la MSE 27, 2005) provided an explicit construction for optimal strategies in repeated games with incomplete information on both sides, in the independent case. In this note, we extend both the duality techniques and the construction of optimal strategies to the dependent case.
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Notes
One may apply Sion’s minmax theorem to the game in mixed strategies when pure strategies are endowed with the product topology, and then apply Kuhn’s theorem to deduce the result. See, e.g., chapter 3 and appendix A in [14] where the same method is applied in the discounted case.
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Acknowledgements
The authors are indebted to Sylvain Sorin and Bernard De Meyer for their insight and suggestions. The authors are also thankful to Mario Bravo for his comments. The first author gratefully acknowledges support from the Artificial and Natural Intelligence Toulouse Institute under Grant ANR-3IA, and funding from the French National Research Agency (ANR), under the Investments for the Future (Investissements d’Avenir) program under grant ANR-17-EURE-0010. The second author gratefully acknowledges funding from the French National Research Agency (ANR), under grant ANR CIGNE (ANR-15-CE38-0007-01).
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Gensbittel, F., Oliu-Barton, M. Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case. Dyn Games Appl 10, 819–835 (2020). https://doi.org/10.1007/s13235-020-00347-y
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DOI: https://doi.org/10.1007/s13235-020-00347-y