On repeated games with imperfect public monitoring: From discrete to continuous time

Mathias Staudigl; Jan-Henrik Steg

doi:10.3934/jdg.2017001

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2017, Volume 4, Issue 1: 1-23. Doi: 10.3934/jdg.2017001

This issue Previous Article Next Article Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs

On repeated games with imperfect public monitoring: From discrete to continuous time

Mathias Staudigl^1, , and
Jan-Henrik Steg^2,

1.
Department of Quantitative Economics, P.O.Box 616, 6200 MD Maastricht, The Netherlands
2.
Center for Mathematical Economics, Bielefeld University, PO Box 10 01 31, 33 501 Bielefeld, Germany

* Corresponding author
* Corresponding author

Received: March 2016

Revised: November 2016

Published: March 2018

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Abstract

Motivated by recent path-breaking contributions in the theory of repeated games in continuous time, this paper presents a family of discrete-time games which provides a consistent discrete-time approximation of the continuous-time limit game. Using probabilistic arguments, we prove that continuous-time games can be defined as the limit of a sequence of discrete-time games. Our convergence analysis reveals various intricacies of continuous-time games. First, we demonstrate the importance of correlated strategies in continuous-time. Second, we attach a precise meaning to the statement that a sequence of discrete-time games can be used to approximate a continuous-time game.

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Mathematics Subject Classification: Primary: 91A25, 91A15; Secondary: 60G57.

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