Splitting games over finite sets

Frederic Koessler, Marie Laclau (), Jérôme Renault and Tristan Tomala

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: 2024
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-03672222v1
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Published in Mathematical Programming, 2024, 203, pp.477-498. ⟨10.1007/s10107-022-01806-7⟩

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Related works:
Working Paper: Splitting games over finite sets (2024)
Working Paper: Splitting games over finite sets (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03672222

DOI: 10.1007/s10107-022-01806-7

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