Cryptocurrency Equilibria Through Game Theoretic Optimization

TL;DR

This paper models cryptocurrency investment equilibria using game theory, analyzing how wealthy investors and governments interact under risk aversion, leading to insights on market capitalization and stability.

Contribution

It introduces a game-theoretic optimization framework to analyze cryptocurrency market equilibria considering government seizure risk and investor behavior.

Findings

Existence and uniqueness of Nash equilibrium established.

Insights into how government policies influence cryptocurrency market capitalization.

Analysis of investor and government strategic interactions.

Abstract

Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure. Speculators constitute another group that tends to introduce volatility and risk for the wealthy. The wealthy must divide their assets between the home currency and the cryptocurrency, while the government decides on the probability of seizing a fraction the assets of this group. Under the assumption that each group exhibits risk aversion through a utility function, we establish the existence and uniqueness of Nash equilibrium. Also examined is the more realistic optimization problem in which the government policy cannot be reversed, while the wealthy can adjust their allocation in reaction to the government's designation of probability. The methodology leads to an understanding the equilibrium market capitalization of cryptocurrencies.