Analyzing the dilemma of countries adopting Bitcoin from the perspective of game theory: how to weigh high returns against high risks?

Author: Chloe, PANews

On July 27, at the 2024 Bitcoin Conference held in Nashville, Tennessee, Trump made a series of commitments, stating that if he is re-elected as president, he will strongly support the future development of Bitcoin and cryptocurrencies. He emphasized that the U.S. must dominate this field, or it will be surpassed by China and other countries. He even mentioned that if elected, he would classify Bitcoin as a national strategic reserve asset, stating, "The federal government will retain all approximately 210,000 Bitcoins currently held, accounting for 1% of the total Bitcoin supply."

However, on July 29, Bitcoin, which had reached the $70,000 mark due to Trump's support, saw its price immediately pulled back from the high point following news of the Biden administration moving Bitcoin. Economist Peter Schiff believes that the Biden administration will sell all Bitcoins before Trump takes office, and the transfer of $2 billion in Bitcoin on the 29th further validated this speculation.

While Trump wants to retain all the Bitcoins currently held by the U.S., the current government immediately sold them off, abandoning the prospect of using this substantial reserve asset as a cornerstone of national strategic reserves. Although Trump's statement on the 27th may become ineffective due to this week's selling event, it has evoked a concept that has existed since the birth of Bitcoin—the game theory of national adoption of Bitcoin.

Is national adoption of Bitcoin advantageous or disadvantageous? What timing for adoption could provide a first-mover advantage? We can understand this through two core concepts in game theory: First Mover Advantage and Payoff Matrix.

Game Theory Concepts: First Mover Advantage and Payoff Matrix

First, there is the First Mover Advantage. Countries that adopt Bitcoin early face both high risks and high rewards. Assuming a Bitcoin economy is established, early adopters will become centers of innovation and investment, attracting businesses in the crypto space and even setting global regulatory standards for digital currencies. Conversely, early adopters also face higher risks, including how to overcome existing regulatory challenges and potential economic instability, creating a situation where the earlier a country acts, the higher the risks and rewards.

Once some influential countries begin to adopt Bitcoin, others will follow suit to avoid being left behind, leading to a herd effect. This effect is driven by the rewards of adopting Bitcoin and the risks of not adopting it. As shown in the following graph, when the Bitcoin adoption cycle enters the steepest part of the S-curve, the herd effect becomes most pronounced.

Next is the Payoff Matrix. Simply put, in game theory, the payoff matrix is used to describe the strategies and payoffs of two or more individuals.

We can use the payoff matrix as a computational tool to display the gains (or losses) of each participant (country) under different strategy combinations. Each participant chooses their best strategy based on the strategies that other participants might adopt. The payoff matrix helps participants analyze and compare the outcomes of different strategies to make optimal decisions.

If we analyze whether countries should adopt Bitcoin using the concept of the payoff matrix, it would look like this:

Assume there are two countries, Country A and Country B, both considering whether to adopt Bitcoin. Each country has two strategies to choose from: adopt or not adopt. The payoff matrix for these two countries can be represented as follows:

In this matrix:

• Each cell represents the payoffs for Country A and Country B after choosing a specific strategy combination.
• The first number in the cell is the payoff for Country A, and the second number is the payoff for Country B.

For example:

• If both Country A and Country B choose to adopt Bitcoin (top left cell), then both Country A and Country B receive a payoff of 10.
• If Country A chooses to adopt while Country B chooses not to (top right cell), Country A receives a payoff of 15, while Country B receives a payoff of 5.

Through such a matrix, Country A and Country B can analyze the outcomes of different strategy combinations and decide on their best strategy based on the possible choices of the other. Ultimately, the matrix can help countries make optimal decisions under uncertain conditions.

For Bitcoin adoption, each country will evaluate the costs and benefits of adopting versus not adopting Bitcoin and choose the best strategy. It goes without saying that, considering the cost/benefit trade-off, the most advantageous strategy is undoubtedly to adopt.

Applying Game Theory Algorithms, Countries Must Identify the Best Response Function

In game theory, the best response function refers to the strategy that maximizes a participant's (country's) payoff given the strategies chosen by other participants (countries). It can be understood as, assuming you are at a card table with an opponent who has already played their cards, how you should optimize the use of the cards in your hand.

In other words, it is the player's best response to the strategies of other players. Therefore, for countries considering adopting Bitcoin, the best response function involves choosing their best strategy based on the expected actions of other countries, which includes considering the economic and geopolitical dynamics of other countries and the resulting impacts.

Thus, the overall logic is as follows: Country A first evaluates the costs and benefits of adopting Bitcoin, including potential economic benefits (such as becoming an innovation center, attracting investment, etc.) and risks (such as regulatory challenges, economic instability, etc.). At the same time, Country A realizes that other countries are also conducting similar cost-benefit assessments. If other countries decide to adopt Bitcoin, this will influence Country A's strategy choice. If Country A expects that all other countries will choose to adopt Bitcoin, then not adopting Bitcoin would put Country A at a disadvantage in competition. Therefore, Country A concludes that it should also accelerate its adoption of Bitcoin to avoid falling behind in the competition.

First Mover Advantage Successfully Reflected in Institutions and Even Countries

To better understand the game theory of national adoption of Bitcoin, we can illustrate it with a few examples: El Salvador, various U.S. states, and MicroStrategy. These examples highlight that the game theory of adoption plays a role in all institutions and even countries.

Since 2021, El Salvador has mined 473 Bitcoins and subsequently recognized Bitcoin as legal tender. The country has gradually allowed many government-related services to be accounted for in Bitcoin, and with the Bitcoins it has purchased, the government has accumulated 5,825 BTC, valued at $394 million.

In May 2024, Wisconsin became the first U.S. state to announce the purchase of Bitcoin. They disclosed in a filing with the Securities and Exchange Commission that they had purchased $160 million worth of Bitcoin ETFs for their pension fund. Although this is not a large amount of capital for Wisconsin's pension fund, which has a total size of $132 billion, it reflects the state's support for using Bitcoin as a reserve asset and the strategic consideration of first-mover advantage.

MicroStrategy is a prime example of first-mover advantage. At the end of 2020, Michael Saylor announced plans to purchase Bitcoin and accumulated 226,000 BTC, accounting for over 1% of the total supply. This was a very unpopular choice at the time in 2020, but now the value of these Bitcoins has nearly doubled, and the company's market capitalization and enterprise value have increased 20-fold and 40-fold, respectively.

Furthermore, from a broader perspective, applying game theory to cryptocurrencies (not limited to Bitcoin) also highlights some advantageous strategies. One such strategy is to adopt stablecoins pegged to the U.S. dollar. Currently, there are 180 fiat currencies in the market, most of which perform worse than Bitcoin. By promoting the adoption of U.S. dollar-pegged stablecoins in economies experiencing currency failure, the position of the dollar in the global economy can be strengthened.