Dynamical Analysis of a Repeated Game with Incomplete Information

DOI10.1287/MOOR.2016.0839zbMATH Open1376.91031arXiv1403.1385OpenAlexW2602817165MaRDI QIDQ4595957

Xavier Bressaud, Anthony Quas

Publication date: 7 December 2017

Published in: Mathematics of Operations Research (Search for Journal in Brave)

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 $frac12leple1$). H"orner, Rosenberg, Solan and Vieille identified an optimal strategy, $sigm{a}^{*}$ for the informed player for $p$ in the range $[frac12,frac23]$. We extend the range on which $sigm{a}^{*}$ is proved to be optimal to about $[frac12,0.719]$ 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.

Full work available at URL: https://arxiv.org/abs/1403.1385

zbMATH Keywords

optimal strategyrepeated game

Mathematics Subject Classification ID

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