Nash Equilibria for Dividend Distribution with Competition

Tiziano de Angelis, Fabien Gensbittel and Stéphane Villeneuve
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Tiziano de Angelis: UNITO - Università degli studi di Torino = University of Turin
Fabien Gensbittel: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements 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
Stéphane Villeneuve: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements 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

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Abstract: We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic game in which two financially-constrained firms operate in the same market. The firms distribute dividends and are faced with default risk. The strategic interaction arises from the fact that if one firm defaults, the other one becomes a monopolist and increases its profitability. The firms choose their dividend distribution policies from a class of randomised strategies and we identify two types of equilibria, depending on the firms' initial endowments. In both situations the optimal strategies and the equilibrium payoffs are found explicitly.

Keywords: Nash Equilibrium; Dividend problem; Free boundary problems; Randomised strategies; Nonzero-sum games; Singular controls (search for similar items in EconPapers)
Date: 2025-09-23
New Economics Papers: this item is included in nep-com, nep-gth and nep-mic
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Published in Mathematics of Operations Research, 2025, ⟨10.1287/moor.2023.0374⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05345639

DOI: 10.1287/moor.2023.0374

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