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Published in: Dynamic Games and Applications 4/2020

07-02-2020

Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case

Authors: Fabien Gensbittel, Miquel Oliu-Barton

Published in: Dynamic Games and Applications | Issue 4/2020

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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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Footnotes
1
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.
 
Literature
1.
go back to reference Aumann RJ, Maschler M (1995) Repeated games with incomplete information, with the collaboration of R. MIT Press, Stearns MATH Aumann RJ, Maschler M (1995) Repeated games with incomplete information, with the collaboration of R. MIT Press, Stearns MATH
5.
go back to reference De Meyer B, Marino A (2005) Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides. Cahiers de la MSE, 27 De Meyer B, Marino A (2005) Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides. Cahiers de la MSE, 27
6.
go back to reference Heuer M (1992) Asymptotically optimal strategies in repeated games with incomplete information. Int J Game Theory 20:377–392 MathSciNetCrossRef Heuer M (1992) Asymptotically optimal strategies in repeated games with incomplete information. Int J Game Theory 20:377–392 MathSciNetCrossRef
7.
go back to reference Mertens J-F, Zamir S (1971) The value of two-person zero-sum repeated games with lack of information on both sides. Int J Game Theory 1:39–64 MathSciNetCrossRef Mertens J-F, Zamir S (1971) The value of two-person zero-sum repeated games with lack of information on both sides. Int J Game Theory 1:39–64 MathSciNetCrossRef
8.
go back to reference Oliu-Barton M (2013) Discrete and continuous time games with incomplete information. Ph.D. thesis, Pierre and Marie Curie University, Paris 6 Oliu-Barton M (2013) Discrete and continuous time games with incomplete information. Ph.D. thesis, Pierre and Marie Curie University, Paris 6
9.
11.
go back to reference Oliu-Barton M (2019) Asymptotically optimal strategies in repeated games with incomplete information and vanishing weights. J Dyn Games 6(4):259–275 MathSciNetCrossRef Oliu-Barton M (2019) Asymptotically optimal strategies in repeated games with incomplete information and vanishing weights. J Dyn Games 6(4):259–275 MathSciNetCrossRef
14.
go back to reference Sorin S (2002) A first course on zero-sum repeated games. Springer, Berlin MATH Sorin S (2002) A first course on zero-sum repeated games. Springer, Berlin MATH
Metadata
Title
Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case
Authors
Fabien Gensbittel
Miquel Oliu-Barton
Publication date
07-02-2020
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 4/2020
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00347-y

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