A game-theoretic analysis of the coexistence and competition between hard and fiat money

This article presents a game-theoretic model analyzing the strategic competition between hard and fiat money, involving a representative player and a consolidated bank (including the central bank). The findings reveal counterintuitive interactions between inflation, interest rates, and monetary policy. When hard money becomes more favorable, through higher interest rates, lower transaction costs, or stronger preferences, the bank responds by withdrawing fiat money, reducing inflation but paradoxically lowering the player's utility. Conversely, increasing the fiat money interest rate leads to money printing and inflation, benefiting both the player and the bank, but ultimately driving hard money out of existence. The model demonstrates how banks use selective fiat money printing and withdrawal to optimize their holdings at the expense of individual players. This study provides insights into currency competition, inflation control, and strategic monetary interventions, relevant for policymakers, financial institutions, and individuals navigating dual-currency economies. By analyzing 26 key parameters, the research uncovers both intuitive and unexpected economic dynamics, offering a structured approach to understanding the power of fiat money in shaping financial systems. These results highlight the importance of monetary policies, transaction costs, and interest rate adjustments in determining the long-term viability of competing monetary systems.