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Pré-Publication, Document De Travail Année : 2021

Splitting games over finite sets

Résumé

This paper studies zero-sum splitting games with finite sets of posterior beliefs. Players dynamically choose a pair {p t , q t } t of martingales of posteriors in order to control a terminal payoff u(p ∞ , q ∞). We introduce the notion of "Mertens-Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens-Zamir system in the unidimensional continuous case. Then, we consider the general case of splitting games with arbitrary contraints and finite sets of posterior beliefs: 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.
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Dates et versions

hal-03166231 , version 1 (11-03-2021)
hal-03166231 , version 2 (16-03-2022)

Identifiants

  • HAL Id : hal-03166231 , version 2

Citer

Frédéric Koessler, Marie Laclau, Jérôme Renault, Tristan Tomala. Splitting games over finite sets. 2021. ⟨hal-03166231v2⟩
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