### AIMS Mathematics

2019, Issue 3: 420-436. doi: 10.3934/math.2019.3.420
Research article

# Establishing cryptocurrency equilibria through game theory

• Received: 02 March 2019 Accepted: 25 March 2019 Published: 07 May 2019
• We utilize optimization methods to determine equilibria of cryptocurrencies. A core group, the wealthy, fears the loss of assets that can be seized by a government. Volatility may be influenced by speculators. The wealthy must divide their assets between the home currency and the cryptocurrency, while the government decides the probability of seizing a fraction the assets of this group. We establish conditions for existence and uniqueness of Nash equilibria. Also examined is the separate timescale 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.

Citation: Carey Caginalp, Gunduz Caginalp. Establishing cryptocurrency equilibria through game theory[J]. AIMS Mathematics, 2019, 4(3): 420-436. doi: 10.3934/math.2019.3.420

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• We utilize optimization methods to determine equilibria of cryptocurrencies. A core group, the wealthy, fears the loss of assets that can be seized by a government. Volatility may be influenced by speculators. The wealthy must divide their assets between the home currency and the cryptocurrency, while the government decides the probability of seizing a fraction the assets of this group. We establish conditions for existence and uniqueness of Nash equilibria. Also examined is the separate timescale 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.

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