A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916465244897280 |
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| author | Dammann, Felix Rodosthenous, Neofytos Villeneuve, Stéphane |
| author_facet | Dammann, Felix Rodosthenous, Neofytos Villeneuve, Stéphane |
| contents | 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 minimizing 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 optimally 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17711 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio Dammann, Felix Rodosthenous, Neofytos Villeneuve, Stéphane Optimization and Control 91A05, 93E20, 90B05 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 minimizing 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 optimally 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. |
| title | A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio |
| topic | Optimization and Control 91A05, 93E20, 90B05 |
| url | https://arxiv.org/abs/2311.17711 |