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

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  • Dammann, Felix
  • Rodosthenous, Néofytos
  • Villeneuve, Stéphane

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.

Suggested Citation

  • Dammann, Felix & Rodosthenous, Néofytos & Villeneuve, Stéphane, 2024. "A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio," TSE Working Papers 24-1481, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:129813
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    References listed on IDEAS

    as
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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