2014/03/06 by Xavier Bressaud, Bressaud, Xavier, Anthony Quas +1
Decision Sciences · Economics, Econometrics and Finance · #91A20 #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1403.1385
openalex publication_date 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \frac 12≤ p≤ 1). Hörner, Rosenberg, Solan and Vieille identified an optimal strategy, σ^* for the informed player for p in the range [\frac 12,\frac 23]. We extend the range on which σ^* is proved to be optimal to about [\frac 12,0.719] 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.