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Markov Games with Frequent Actions and Incomplete Information—The Limit Case

Cardaliaguet, Pierre; Rainer, Catherine; Rosenberg, Dinah; Vieille, Nicolas (2013), Markov Games with Frequent Actions and Incomplete Information—The Limit Case, Mathematics of Operations Research, 41, 1, p. 49-71. 10.1287/moor.2015.0715

Type
Article accepté pour publication ou publié
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https://hal.archives-ouvertes.fr/hal-00843475
Date
2013-07
Nom de la revue
Mathematics of Operations Research
Volume
41
Numéro
1
Éditeur
Institute of Management Sciences
Pages
49-71
Identifiant publication
Métadonnées
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Auteur(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rainer, Catherine
Laboratoire de Mathématiques [LM-Brest]
Laboratoire de mathématiques de Brest [LM]
Rosenberg, Dinah
Groupement de Recherche et d'Etudes en Gestion à HEC [GREGH]
Vieille, Nicolas
Groupement de Recherche et d'Etudes en Gestion à HEC [GREGH]
Résumé (EN)
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.
Mots-clés
Markov games; incomplete information; zero-sum games; Hamilton-Jacobi equations; repeated games