Establishing cryptocurrency equilibria through game theory

Carey Caginalp; Gunduz Caginalp; Carey Caginalp; Gunduz Caginalp

doi:10.3934/math.2019.3.420

AIMS Mathematics

2019, Volume 4, Issue 3: 420-436. doi: 10.3934/math.2019.3.420

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Research article

Establishing cryptocurrency equilibria through game theory

Carey Caginalp ^{1,2
,
,},
Gunduz Caginalp ¹

1.
University of Pittsburgh, Mathematics Department, 301 Thackeray Hall, Pittsburgh, PA, USA
2.
Chapman University, Economic Science Institute, 1 University Drive, Orange, CA, USA

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.
- mathematical finance,
- game theory,
- cryptocurrency,
- optimization
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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Abstract

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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