A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio

Felix Dammann, Neofytos Rodosthenous and Stéphane Villeneuve
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Felix Dammann: Center for Mathematical Economics, Bielefeld University
Neofytos Rodosthenous: Center for Mathematical Economics, Bielefeld University
Stéphane Villeneuve: Center for Mathematical Economics, Bielefeld University

No 730, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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: 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 (search for similar items in EconPapers)
Pages: 31
Date: 2025-08-14
New Economics Papers: this item is included in nep-mic
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