Dynamical Analysis of a Repeated Game with Incomplete Information

Xavier Bressaud () and Anthony Quas ()
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Xavier Bressaud: Université Paul Sabatier, Institut de Mathématiques de Toulouse, F-31062 Toulouse Cedex, France
Anthony Quas: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 2Y2

Mathematics of Operations Research, 2017, vol. 42, issue 4, 1085-1105

Abstract: We study a two player repeated zero-sum game with asymmetric information introduced by Renault in which the underlying state of the game undergoes Markov evolution (parameterized by a transition probability, p , in the range 1 2 to 1). Hörner, Rosenberg, Solan and Vieille identified an optimal strategy, σ * for the informed player for p in the range [ 1 2 , 2 3 ] . We extend the range on which σ * is proved to be optimal to about [ 1 2 , 0.719 ] and prove that it fails to be optimal at a value around 0.7328. Our techniques make use of tools from dynamical systems, specifically the notion of pressure, introduced by D. Ruelle.

Keywords: repeated game; optimal strategy (search for similar items in EconPapers)
Date: 2017
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