A stochastic non-zero-sum game of controlling the debt-to-GDP ratio

Felix Dammann, Néofytos Rodosthenous and Stéphane Villeneuve
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Felix Dammann: Universität Bielefeld = Bielefeld University
Néofytos Rodosthenous: UCL - University College of London [London]
Stéphane Villeneuve: 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

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Abstract: We introduce a non-zero-sum game between a government and a legislative body to study the optimal level of debt. Each player, with different time preferences, can intervene on the stochastic dynamics of the debt-to-GDP ratio via singular stochastic controls, in view of minimiz-ing non-continuously differentiable running costs. We completely characterise Nash equilibria in the class of Skorokhod-reflection-type policies. We highlight the importance of different time preferences resulting in qualitatively different type of equilibria. In particular, we show that, while it is always optimal for the government to devise an appropriate debt issuance policy, the legislator should opti-mally impose a debt ceiling only under relatively low discount rates and a laissez-faire policy can be optimal for high values of the legislator's discount rate.

Keywords: Non-zero-sum game; Singular stochastic control; Free-boundary problem; Debt-to-GDP ratio (search for similar items in EconPapers)
Date: 2025-02-17
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