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Cryptocurrency Equilibria Through Game Theoretic Optimization

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  • Carey Caginalp
  • Gunduz Caginalp

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.

Suggested Citation

  • Carey Caginalp & Gunduz Caginalp, 2018. "Cryptocurrency Equilibria Through Game Theoretic Optimization," Papers 1805.10128, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1805.10128
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    Cited by:

    1. Guizhou Wang & Kjell Hausken, 2021. "Governmental Taxation of Households Choosing between a National Currency and a Cryptocurrency," Games, MDPI, vol. 12(2), pages 1-24, April.
    2. Alla Petukhina & Simon Trimborn & Wolfgang Karl Härdle & Hermann Elendner, 2021. "Investing with cryptocurrencies – evaluating their potential for portfolio allocation strategies," Quantitative Finance, Taylor & Francis Journals, vol. 21(11), pages 1825-1853, November.

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