A Game-Theoretic Approach to Bitcoin’s Valuation in Equilibrium

Gresham's law is frequently cited in discussions about bitcoin and its use or lack thereof as a currency. However, it's argued that applying Gresham's law to explain bitcoin's minimal circulation as a medium of exchange is fundamentally flawed. The basis for this argument is that Gresham's law applies specifically to physical currencies that are in circulation simultaneously and share the same nominal value but differ in their intrinsic value. This discrepancy between nominal and intrinsic values compels people to spend the currency with lesser intrinsic value while hoarding the one with greater worth.

The assertion that people prefer to spend fiat currency over bitcoin, thereby saving bitcoin, echoes the principles observed in Gresham’s law but diverges in application due to the nature of bitcoin being a digital rather than a physical currency. This behavior towards bitcoin can be seen as intuitive and has been widely observed and discussed within financial circles. The inclination to hold onto bitcoin instead of using it for transactions can be attributed to its perceived value and potential for appreciation, not necessarily the dynamics between competing currencies with equal face values as outlined by Gresham's law.