Effective coordination between fiscal and monetary policy is crucial for macroeconomic stability, yet achieving it presents significant challenges due to differing objectives and institutional setups. This study evaluates the strategic interaction between fiscal and monetary authorities in Hungary from 2013 to 2023, employing the Nash equilibrium framework under the assumption of non-cooperative behavior. By modeling the authorities as independent players optimizing distinct payoff functions based on key economic indicators (interest rates, government spending, inflation, output gap, fiscal deficit, and public debt), the analysis estimates the best response strategies and computes the resulting Nash equilibrium. The key findings reveal persistent deviations between actual policies and the computed equilibrium strategies. Specifically, actual fiscal policy was consistently more expansionary (average actual deficit −2.6% to 7.6% GDP vs. equilibrium recommendations ranging from 8.5% surplus to −3.0% deficit) than the Nash equilibrium indicated, particularly during periods of economic growth. Monetary policy often lagged in equilibrium recommendations, maintaining low interest rates (e.g., 0.9% actual vs. 11.5% equilibrium in 2019) before implementing sharp increases (13% actual vs. approx. 3.5–3.8% equilibrium in 2022–2023) that significantly overshot the equilibrium. These misalignments underscore potential suboptimal outcomes arising from independent policymaking, contributing to increased public debt and heightened inflationary pressures in the Hungarian context. This study highlights the potential benefits of aligning policies closer to mutually consistent strategies, suggesting that improved coordination frameworks could enhance macroeconomic stability, offering insights relevant to Hungary and similar economies.