Competition between variable-supply and fixed-supply currencies

For one variable-supply currency in isolation, one player's Cobb-Douglas utility depends on the current supply divided by the initial supply, multiplied by the inverse of the accumulative inflation/deflation. With equal weight assigned to both factors, money printing outweighs inflation, and money withdrawal outweighs deflation. The study design is to analyze how competition between one variable-supply and one fixed-supply currency impacts the player's choice of currency. Applying the 1959-2021 US M2 money supply data and the 1635-2021 US inflation data, the player's utility increases over time when assigning high weight to money printing/withdrawal and increases less or decreases overall when assigning high weight to inflation/deflation. With different player support for the two currencies, depending on each currency's backing, convenience, confidentiality, transaction efficiency, financial stability, and security, replicator dynamics is used to determine the player's volume fraction of transactions in each currency. Low, high, increasing, and decreasing support of a currency are analyzed. Each fraction may increase, decrease, be inverse U-shaped, U-shaped, and approach low or high levels over time. For example, high weight assigned to money printing may cause the player to eventually prefer the variable-supply currency unless the player supports the fixed-supply currency highly and increasingly.