According to Sergei Bondarenko, head of the Department of Technology and Integration of Deloitte Ukraine, it was thanks to the mathematical discipline of the game theory that the current blockchain revolution became possible. What role does one of the most widely used economic theories play in the crypto economy, and how can the effectiveness of the results of actions be calculated using tools based on another popular notion of modern economic science known as the Pareto principle?

## Introduction to the Game Theory

The game theory is a section of the mathematical economy that studies the solution of conflicts between the parties and considers the optimality of the strategies they apply. The game theory considers the logic of decision-making among people, animals, and computer systems. So, in politics, the game theory is used to predict the reactions of certain nations to a particular event. In military operations, the game theory considers possible actions of an opponent. And in financial markets, the game theory is used to analyze the stock market. In the crypto world, the game theory considers the consequences of potential cyber attacks. And when developing cryptocurrencies, the game theory can predict the reaction of token holders to certain incentive measures.

Thus, cryptography is used to prove the work done in the blockchain, and the game theory is applied to achieve the desired behavior of players in the future. Most often, the game theory consists of three components:

Players are decision-makers;

Strategies are decisions that the parties make to achieve the desired goals;

Payouts are the result of a strategy.

The game theory allows you to create networks with predefined characteristics that will encourage players to behave in a certain way. So, in blockchain there can be three types of players, who are the developers, users, and miners, each of whom can perform only certain actions. Developers are responsible for the work and development of the network, users carry out transactions in it, and miners maintain the network. According to the game theory, no player can change their strategy of behavior to achieve the desired result, if other participants in the strategy do not change, which maintains order and compliance with the rules in any blockchain.

Consider, for example, a situation in which two sides are to negotiate the results of the development of potential situations depending on their decisions. For each situation below are graphs of the results and possible payments, where a vertical axis is assigned for player 1, and the horizontal for player 2. Suppose that the negotiations can have four possible outcomes: a, b, c, and d. And also that possible payments to players in the first situation will be equal:

a: π1 = 1, π2 = 2

b: π1 = 3, π2 = 3

c: π1 = 4, π2 = 5

d: π1 = 6, π2 = 7

For the second situation, possible payments to players in making various decisions will be equal:

a: π1 = 6, π2 = 2

b: π1 = 4, π2 = 4

c: π1 = 3, π2 = 5

d: π1 = 1, π2 = 7

Thanks to these graphs, we can answer the following questions:

What outcomes will be considered Pareto efficient?

What conclusions can be drawn about the social order (cooperation and coordination)?

Which of the games will develop in these situations, the game of "common interests" or the game of "conflict of interests?"

## The First Situation

General payments: a = 3, b = 6, c = 9, d = 13.

When we calculate the total payouts for each result, only option d is Pareto efficient. It is worth noting that in this situation, the graph goes up and to the right, which means that with each subsequent decision, the total payment increases compared to the previous one. This is called the Pareto ranking.

By evaluating these results, we can also answer the question of whether the players will work together in order to achieve the best results presented in option d. The answer is yes. This is called a game of common interests. A good example of a game of common interests will be a traffic jam on the road. Traffic jams are in most cases an undesirable result, which is why most people are interested in avoiding such a result, thereby having a common interest.

As for the two problems of the social order, the lack of cooperation and the lack of coordination, in this example, only coordination is lacking. In the real world, this happens infrequently, and usually the lack of cooperation between the parties is added to the coordination problem, as in the second example.

## The Second Situation

General payments: a = 8, b = 8, c = 8, d = 8.

When calculating the total payments, we see that each outcome of the situation is Pareto efficient. In the example of the distribution of Bitcoin in the game theory, described below, in two cases players receive Bitcoins in the ratio 6-0-0 and 2-0-4, which is considered to be an extremely disproportionate distribution of the payout, and in real life can lead to the development of a potential conflict situation.

As for the problems of social order, the lack of cooperation and the lack of coordination, in this example, there are both. This means that it will be much more difficult to organize a social order in this situation.

When considering practical examples, there are usually certain parts of both conflict and general interest. In our example, for all possible outcomes, the transition from the situation c → b involves only the coordination problem, while the transitions c → a and c → d involve both problems.

It should be noted that the game theory is a complex science that includes many components and possible scenarios for the development of games, which all require detailed study for full application in practice. Even with general ideas about this tool, however, it is easy to understand its importance in work and further development of the crypto economy.

## Pareto Efficient Results

The Pareto principle is one of the central concepts of modern economic science, which is used to evaluate the effectiveness of any activity. By using the Pareto principle in the crypto economy, players can calculate the most effective behavioral strategies to achieve the desired results: launching projects, calculating costs, evaluating the interaction of various parties, and so on.

Victor Makarskyy, the developer of protocols for decentralized networks, figured out how Pareto efficiency can be used to analyze the possible outcomes of actions.

Imagine that the developer is faced with the task of launching a new set of protocols for a blockchain company. One of the key issues that the protocol developers will need to answer is how to create an option in which interactions between the parties lead to the best overall result and which can also be considered "socially useful." Moreover, it will be necessary to understand what exactly is meant by the "socially useful" protocol within the framework of this company and how to evaluate this indicator.

One of the evaluation criteria will be the indicator of the effectiveness of this protocol. Namely, how effectively resources are allocated in it and whether this effectiveness is achieved in each case, regardless of the nature of the interaction.

Ideal results, in this case, will be those that:

Maximize total payments (total profit or benefit) in comparison with other possible outcomes.

Will be preferable for all parties (subjects of economic relations) in comparison with other possible outcomes.

Note that each of the requirements refers to a conditional comparison between two different results of an action. The movement from the potential result A to the potential outcome B, at which the most practical value will be obtained, lies at the heart of the game theory.

The situation when Pareto efficiency is achieved in the economy is the situation when all the benefits from the exchange of parties are exhausted, and further improvement is impossible, meaning there is no possible outcome in which, using available resources and technologies, one of the parties improves their position without harm or deterioration to the position of another. In other words, there will always be winners and losers from the outcome of situation A to the outcome of situation B. According to the concept of Pareto efficiency, even though losers appear, the winners can create conditions for the compensation of losses, thereby creating "socially useful" results.

In this table, the practical value (U) for each side (1, 2, and 3) obtained from the possible outcomes of situations A, B, C, D, and E is shown. Thus, in the performance of some actions and the transition from the results of A to the results B, C, D, and E, each side receives a different amount of value, or a different level of satisfaction (U).

Pareto efficiency (PE) is revealed when evaluating improvements in a variety of possible outcomes. Thus, it turns out:

Variant B is Pareto efficient, since, in the transition B → C 3, the side receives 60 → 50;

The same goes for option C 25 and 50 are the maximum values of U for sides 1 and 2;

With the transition D → C, side 3 gets 70 → 50, and therefore D is Pareto efficient, which happens also for D → B, where side 3 gets 70 → 60;

In this case, with the A → C transition, all parties get the same or better results, which means that A is not Pareto efficient;

The same happens when E → D, where variant E is not Pareto efficient.

Now the same thing with the Bitcoins. Imagine that I, you, and Sarah have 6 Bitcoins received for nothing. Under different scenarios, the distribution of these Bitcoins will look like this:

In this case, the total sum of Bitcoins is expressed in the total income (total surplus). In this connection it turns out:

A = 6, B = 6, C = 5, D = 6, E = 6.

All actions where we get 6 Bitcoins as a result are Pareto optimal with the maximum results for the group since a larger value is impossible. Also, with option A, you get all the Bitcoins, while the other parties have 0. Even so, option A remains Pareto optimal and "socially useful," although it is unfair to all parties.

## Conclusion

Using these tools of mathematical analysis and forecasting the results of actions, any player will be able to understand the logic of the work of cryptocurrencies, the construction of blockchains, and the development principles of the crypto economy as a whole. It was because of the game theory that Satoshi Nakamoto was able to combine cryptography, distributed ledger system, and digital currencies into a single Bitcoin network and launch a revolution in traditional financial markets.