Competitive Equilibrium for Bitcoin Mining

Understanding the group effect and deriving an equilibrium

Bitcoin mining is like a race in some ways. You want to be faster than anyone else, and your chance of winning depends on your competition.

Bitcoin miners need to invest time and effort in order to obtain future cash flows. However, they do not act in isolation. Competing market participants may simultaneously pursue the discovery of a cryptocurrency via costly exploration. They may also affect the total supply and market price.

Nowadays cryptocurrency mining requires a rising power consumption. In some cases, depending on the prevailing market price, the mining cost even exceeds the reward for some miners.

The performance of a chosen action is affected by the corresponding choices of others. As a consequence, the group effect of other participants must be taken into account when deciding an optimal strategy.

Mean-Field Equilibrium

In a recent paper, we analyze the competitive equilibrium for markets with a very large number of competitors, like bitcoin mining. We consider a collection of agents that are able to expend costly effort continuously through time, and each agent is rewarded for their effort at a random time by receiving a stream of cash flows.

The time until the cash flows begin for a particular agent can be shortened, although it remains random, by expending more effort. As more participants succeed in generating income, the reward for any particular participant may diminish.

We work in a mean-field setting with a continuum of agents and search for a mean-field Nash equilibrium.

In such an equilibrium, the dynamics of population entry into the state of receiving cash flows is determined by the aggregate strategies of all agents, and under these dynamics no individual agent can improve their performance by altering their strategy.

We analyze the problem under three different specifications for the cash flow horizon: (i) finite, (ii) random (exponentially distributed), and (iii) infinite. When the horizon is exponentially distributed or infinite, we are able to find a class of equilibria in closed form parameterized by two real numbers. The specification which is used depends on the context of the problem being modeled.

Analyzing the behavior of equilibrium with respect to input parameters produces some initially counterintuitive results. For example, in some cases an increase in the cost of an agent’s effort to receive cash flows can increase the value function rather than decrease it as might be expected. This is a result of the endogenous structure of cash flows in equilibrium caused by competition.

There are many directions for future research. To facilitate research collaboration and strategic partnership between CFRM and the industry, the CFRM Quantitative Analytics Lab (QAL) is created to focus on the design and development of quantitative models, analytical tools, and algorithms to solve problems in the finance industry and beyond. For new collaborative projects on cryptocurrency, reach out to the QAL director here.

Disclaimer: this is not intended to be investment advice.

Reference

Effort Expenditure for Cash Flow in a Mean-Field Equilibrium [pdf], International Journal of Theoretical & Applied Finance, Vol. 22, №04, p.1950014, 2019

For more, follow/connect on Linkedin: https://www.linkedin.com/in/timstleung/

Disclosure: Interactive Brokers

Information posted on IBKR Traders’ Insight that is provided by third-parties and not by Interactive Brokers does NOT constitute a recommendation by Interactive Brokers that you should contract for the services of that third party. Third-party participants who contribute to IBKR Traders’ Insight are independent of Interactive Brokers and Interactive Brokers does not make any representations or warranties concerning the services offered, their past or future performance, or the accuracy of the information provided by the third party. Past performance is no guarantee of future results.

This material is from Computational Finance and Risk Management, University of Washington and is being posted with permission from Computational Finance and Risk Management, University of Washington. The views expressed in this material are solely those of the author and/or Computational Finance and Risk Management, University of Washington and IBKR is not endorsing or recommending any investment or trading discussed in the material. This material is not and should not be construed as an offer to sell or the solicitation of an offer to buy any security. To the extent that this material discusses general market activity, industry or sector trends or other broad based economic or political conditions, it should not be construed as research or investment advice. To the extent that it includes references to specific securities, commodities, currencies, or other instruments, those references do not constitute a recommendation to buy, sell or hold such security. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.

In accordance with EU regulation: The statements in this document shall not be considered as an objective or independent explanation of the matters. Please note that this document (a) has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and (b) is not subject to any prohibition on dealing ahead of the dissemination or publication of investment research.

Any trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations.

Disclosure: Digital Assets

Trading in digital assets, including cryptocurrencies, is especially risky and is only for individuals with a high risk tolerance and the financial ability to sustain losses. Eligibility to trade in digital asset products may vary based on jurisdiction.