Fiscal and Monetary Equilibrium: A Differential Game Between the Government and the Central Bank

Document Type : Research Article

Authors

1 Department of Mathematics, Semnan University, Semnan 35195-363, Iran

2 Department of Mathematics, Semnan University, Semnan 35195-363, Iran; Department of Mathematics, Washington University, St.Louis, MO, USA

Abstract

This study employs a differential game-theoretic framework to analyze the strategic interaction between the government and the central bank in the context of public debt management. The core objective is to develop an analytical model that stabilizes government debt by optimizing three critical policy instruments: tax revenue, government spending, and the money supply. A major innovation of this research lies in disaggregating the fiscal deficit into two distinct control variables—taxation and spending, which allows for the derivation of optimal equilibrium trajectories for each. Numerical simulations, based on a 20-year dataset from the United States, reveal key differences in outcomes depending on the degree of independence or interdependence between fiscal instruments. When tax revenue and government spending are treated as independent from the monetary authority, the model converges to equilibrium values of 0.8992 for public debt, 0.0982 for the fiscal deficit, and 0.1288 for the monetary base. Conversely, when tax and spending decisions are jointly determined as components of the fiscal deficit, the corresponding equilibrium values shift slightly to 0.8975, 0.0852, and 0.1157, respectively. These findings suggest that enhanced coordination between the fiscal authority’s instruments and the central bank’s control over money creation can improve debt sustainability and overall macroeconomic stability. While the empirical focus is on the U.S. economy, the proposed framework offers a flexible foundation for evaluating fiscal-monetary dynamics in other institutional settings.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 1
May 2024
Pages 133-149

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History

  • Receive Date: 04 March 2025
  • Revise Date: 11 May 2025
  • Accept Date: 14 May 2025
  • Publish Date: 08 August 2025

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