Markov Games with Frequent Actions and Incomplete Information

37 Pages Posted: 25 Oct 2013 Last revised: 24 Jun 2015

Pierre Cardaliaguet

Université Paris Dauphine

Catherine Rainer

l’Université de Brest en France

Dinah Rosenberg

HEC Paris - Economics & Decision Sciences

Nicolas Vieille

HEC Paris - Economics & Decision Sciences

Date Written: October 24, 2013

Abstract

We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.

Suggested Citation

Cardaliaguet, Pierre and Rainer, Catherine and Rosenberg, Dinah and Vieille, Nicolas, Markov Games with Frequent Actions and Incomplete Information (October 24, 2013). HEC Paris Research Paper No. ECO/SCD-2013-1007. Available at SSRN: https://ssrn.com/abstract=2344780 or http://dx.doi.org/10.2139/ssrn.2344780

Pierre Cardaliaguet

Université Paris Dauphine ( email )

PARIS
France

Catherine Rainer

l’Université de Brest en France ( email )

Brest
France

Dinah Rosenberg

HEC Paris - Economics & Decision Sciences ( email )

Paris
France

Nicolas Vieille (Contact Author)

HEC Paris - Economics & Decision Sciences ( email )

Paris
France

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