Non-cooperative Interactions Between Government and Central Bank in Public Debt Management: A Differential Games Approach

Document Type : Scientific paper

Authors

Department of Mathematics, Semnan University, Semnan, Iran

10.22080/mrl.2025.27630.2109

Abstract

The government and the central bank are among the most important components of a country’s economic structure. The steady-state values of key macroeconomic variables such as public debt (comprising government expenditures and tax revenues) and the monetary base are jointly determined by the behavior and policy strategies of both institutions. Accordingly, this study presents a non-cooperative game-theoretic model based on linear-quadratic (LQ) control to determine the optimal values of these variables. In this model, the government and the central bank are considered as two strategic players, each pursuing its own objectives through its respective policy instruments.In the proposed framework, government expenditures and tax revenues are modeled separately, replacing the conventional fiscal deficit variable. This allows for the independent computation of their optimal (steady-state) values and their respective convergence dynamics over time. Numerical simulation results show that the nature of the relationship between the government’s fiscal control instruments (expenditures and tax revenues) significantly influences the equilibrium outcomes of the model. When these two variables are introduced as interdependent, public debt, fiscal deficit, and the monetary base all decrease significantly, and the convergence speed toward equilibrium improves. The findings indicate that greater coordination between fiscal policy (government expenditures and tax revenues) and monetary policy can lead to better macroeconomic outcomes. Such coordination contributes to lower public debt, improved fiscal sustainability, and more effective control of inflation and liquidity. Furthermore, comparing the results of non-cooperative, cooperative, and Stackelberg game structures shows that the Stackelberg case—where the government acts as the leader and the central bank as the follower -yields superior outcomes in reducing the fiscal deficit, controlling the monetary base, stabilizing public debt, and accelerating convergence to equilibrium.

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References

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Macroeconomics Research Letter
Volume 20, Issue 46
August 2025
Pages 73-106

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History

  • Receive Date: 23 August 2024
  • Revise Date: 29 June 2025
  • Accept Date: 21 July 2025

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