Splitting games over finite sets

Frederic Koessler, Marie Laclau (), Jérôme Renault () and Tristan Tomala
Additional contact information
Jérôme Renault: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Tristan Tomala: HEC Paris - Ecole des Hautes Etudes Commerciales, GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique

PSE-Ecole d'économie de Paris (Postprint) from HAL

Abstract: This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {pt,qt}t, in order to control a terminal payoff u(p∞,q∞). A first part introduces the notion of "Mertens–Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens–Zamir system for continuous functions on the square [0,1]2. A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (Math Oper Res 45:1237–1257, 2020), we show that the value exists by constructing non Markovian ε-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions.

Keywords: Splitting games; Mertens-Zamir system; Repeated games with incomplete information; Bayesian persuasion; Information design (search for similar items in EconPapers)
Date: 2022
New Economics Papers: this item is included in nep-gth and nep-mic
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03672222
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Published in Mathematical Programming, inPress, ⟨10.1007/s10107-022-01806-7⟩

Downloads: (external link)
https://shs.hal.science/halshs-03672222/document (application/pdf)

Related works:
Working Paper: Splitting games over finite sets (2022)
Working Paper: Splitting games over finite sets (2022)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03672222

DOI: 10.1007/s10107-022-01806-7

Access Statistics for this paper

More papers in PSE-Ecole d'économie de Paris (Postprint) from HAL
Bibliographic data for series maintained by Caroline Bauer ().