The Theory of the Evolution of Economic Relations as an Approach to

Generalize the Theory of Games

ASHIKHMIN VICTOR, SHABAROV VLADIMIR

“PHOTOCOR INSTRUMENTS” Ltd.,

Tallinn, Jõe tn 5, 10151,

ESTONIA

Abstract: - The Theory of Games in the classical sense uses the idea of a system of economic relations of one

type, namely economic relations of a private nature when the goal of rational behavior of the subject of

economic relations (ER) is to maximize the benefit (own profit). In the process of evolution, economic relations

go through several stages (namely 16), and for each stage, the set of characteristics of the basic elements strictly

differs from the set of other stages. The rational behavior of the subjects is largely determined by this particular

set of characteristics. Thus, the corresponding Theory of Rational Behavior of Economic Subjects (TRES) is

the generalization of the Theory of Games for application in economics (that is, it applies not only to one type

of economic relations, aiming at private benefit). Another aspect of the generalization of the Theory of Games

in conditions of global information and computer accessibility is the transition from money as a medium of

exchange that was a “transferable numerical utility” to another medium of exchange - a full range of goods with

the complete dynamically changing set of exchange coefficients as a “generalized medium of exchange” that

organically corresponds to the economic content of the production process.

Key-Words: - economic relations, game theory, rational behavior, evolution, private nature, public nature.

Received: March 29, 2023. Revised: January 2, 2024. Accepted: January 24, 2024. Published: February 16, 2024.

1 Introduction

The works of J. Von Neumann, including, [1], are

fundamental in the field of game theory. His results

are used in a variety of fields - from algebraic

topology, biology, and meteorology to military

affairs, [2], [3], [4], [5]. This widespread use is

because the concept of competition or rivalry that

underlies the Theory of games is typical for a huge

number of similar applied areas.

The area of our study is economics in a broader

sense than the “game” between a buyer and a seller,

that is, one in which “rational” behavior does not

aim to maximize one’s benefit.

Therefore, all the results obtained in this study

do not apply to other fields, such as, for example,

military affairs.

To be more precise, in this article, we are not

considering the Theory of Games itself, but the

Theory of Rational Behavior of Economic Subjects

(TRES). The Theory of Games is a special case of

TRES.

Our goal is to formulate precisely the approach

to generalizing the Theory of Games, but not to

create the generalized theory itself.

2 Problem Formulation

The term “Generalization” in this work refers to the

expansion of the Theory of Games for application at

the stages of evolution of economic relations which

differ from those considered by von Neumann's

“competitive” economic relations, characterized by

the desire for the subjects to maximize their profit.

To be precise, the generalization of the Game

Theory should describe the rational behavior of a

participant in economic relations, where each act of

economic interaction does not aim at the profit

maximization of the participating economic entities,

but at the maximization of utility for the entire

economic community as a whole.

At the same time, the focus of the Generalized

Theory of Games shifts from describing the rational

behavior of players to:

- description of the usefulness of the economic act

for the community based on the knowledge of the

utility for each of the subjects and the usefulness

of the subject for the community,

- description of the rational behavior of the

subjects in the sense of “social” utility.

Thus, it would be correct to talk about the

generalization of the Theory of Games for evolving

economic relations, which could be called the

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

676

Volume 21, 2024

Theory of “rational” behavior of economic subjects

(TRES).

Von Neumann and Morgenstern developed the

Theory of Games for use in economics based on a

set of hypotheses about basic economic concepts.

This set of hypotheses and concepts characterizes

one particular case in the series of successive stages

in the evolution of economic relations.

Thereby the theories of “rational” behavior of

the subjects of economic relations, based on the

characteristics of economic categories for each stage

of development of economic relations present the

generalization of von Neumann’s Theory of Games.

It should be noted that the basic hypothesis for both

theories is the hypothesis of contradiction between

the subjects of ER. In the Theory of Games, the

opposite goals of economic entities present the form

of such a contradiction. In TRES, we consider the

existence of the property of independence between

economic agents as a main contradiction.

3 Problem Solution

Throughout the history of mankind, economic

relations have been developing in one way or

another, each time going through the stages

described, for example, in [6].

Relying on the laws of evolution of economic

relations, specifically on the structure of removing

the quality of independence of the subjects of

economic relations, [7], we will indicate the stages

of evolution of economic relations throughout the

entire period of human history.

Since the generalization of the Theory can be

carried out based on different grounds, the most

important proof of the correctness of the approach to

the generalization of the Theory is the precise

formulation of the research methodology.

In this work, we use the following methodology

for the Theory of the evolution of economic

relations building:

I. Establishing the boundaries of the phenomenon

under study - economic relations by identifying pre-

economic relations from the whole set of

"economically similar" phenomena.

II. Identification of the initial concept of pre-

economic relations (“Impact and Appropriation” –

the dialectical pair containing the developing

contradiction).

III. Formulating a hypothesis about the essence of

the contradiction that serves as the cause and driving

force for the development of economic relations

(independence of economic entities).

IV. Obtaining the exhaustive list of forms of

PrER (4 forms in total) when carrying out the

minimum possible acts of development of the initial

concept of pre-economic relations. The highest form

is one where the property of independence between

Impact and Assignment is removed to the limit - to

the point of their complete dependence.

V. We introduce into the scope of consideration the

interaction between subjects and, thereby, move on

to the study of economic relations. As a result, we

obtain four forms of economic relations (Initial

Economic Relations, IER) from four forms of pre-

economic relations.

VI. In connection with the emergence in the

field of research on relationships where more than

one subject is involved, we introduce a new concept

that is impossible in pre-economic relations,

namely, the nature of the economic relationship

(private or public). The private nature indicates the

independence of the subjects in this regard. Public

character indicates the dependence of subjects in the

relationship.

VII. We carry out the minimum possible acts of

development similar to the process of pre-economic

relations development. Namely, we consider four

IERs, in which the social character extends to

increasingly higher forms of IERs. We receive the

exhaustive list of 16 types of Systems of Economic

Relations, which indicates all types of economic

relations both in the past, and the present and future.

In this work, we solve the following problems:

a. It is necessary to consider economic

relations throughout the history of mankind.

From the emergence of economic relations

in the past to the future forms of economic

relations;

b. It is necessary to establish a criterion

indicating precisely the development

(qualitative leaps) of economic relations;

c. Using this universal criterion, it is necessary

to compile the exhaustive list of main forms

of economic relations development (stages,

formations);

d. It is necessary to indicate for what forms of

economic relations the Theory of Games is

applicable and for what ones it is not;

e. We have to specify the main features of the

TRES for the forms of economic relations

for which the Theory of Games is not

applicable.

3.1 Based Concepts

As a method for studying the development of

economic relations, we use dialectics, which

describes changes (leaps) in the forms of a certain

phenomenon through its internal contradictions,

which are overcome (dialectically eliminated) in

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

677

Volume 21, 2024

each of the subsequent forms of development of this

phenomenon.

In this paper, we accept the following hypotheses:

- the most elementary form of the phenomena of

“the Economic Relations" is the “Impact and

Appropriation”;

- the cause for the Development of Economic

Relations (contradiction developing ER) is the

property of Independence of the parties in

Economic Relations;

- the purpose of “the Development" is to eliminate

(dialectically remove) the Property (Quality) of

Independence of the parties. Thus, the parties

(economic agents) become dependent.

The Theory of evolution of economic relations,

[6], is based on the definition of pre-economic

relations (PrER) and the analysis of their

transformation into economic relations.

System-forming properties that distinguish pre-

economic relations from economic ones are:

- exclusively individual (private) labor, and not the

division of labor, as it occurs in economic

relations (transition from singular to plural).

The transition of pre-economic relations into

economic relations occurs according to this criterion

of division of labor.

3.2 Developing a Theory of the Evolution of

Economic Relations

To systematically obtain a complete variety of types

of economic relations and identify all stages of their

evolution, the principle of dialectics is used, [8].

According to this principle, any type of

evolution includes pairs of fundamental concepts

that are somewhat similar to each other, but also

having a contradiction that is the cause of evolution.

Another important dialectical principle is that each

stage of evolution contains all its previous stages in

some sublated form. The transition from singular to

plural is also an important evolutionary principle.

Using this methodology, we highlight the

following four basic elementary forms-stages of the

evolution of pre-economic relations between a

person and the objects of nature:

Using this methodology, we identify the

following four basic elementary forms - the stages

of the evolution of pre-economic relations between

humans (subject) and nature (object):

- independent (not mutually dependent)

Appropriation and Impact,

- Exchange “subject-object” as an interrelated

(mutually dependent) Appropriation – Impact,

- Concentration - Distribution as a set of

Exchanges of "one subject with many objects" or

"many subjects with one object",

- Production as a network of all preceding forms

including Interdependent Concentration –

Distributions (the relations "many subjects –

many objects").

Stage 1. Independent Impact and Appropriation. Our

first hypothesis is that this is the most elementary

form of the phenomenon being studied and this is

depicted in Figure 1. A subject can appropriate an

object of nature that is not the result of human

impact. And vice versa, the Subject can exert an

impact not for appropriation, but, for example, just

out of curiosity.

Fig. 1: Independent Impact and Appropriation

Stage 2. Exchange as an interdependent

Appropriation – Impact. The simplest step in the

evolution of the first stage is the transformation to

the interdependent Impact/Appropriation which is

shown in Figure 2. Stage 2 is the form of

relationship when the result of the Impact causes the

Appropriation (IA exchange), and the form of

relationship when the result of the Appropriation

causes the Impact (AI exchange).

Fig. 2: Exchange as an interdependent

Appropriation – Impact

Stage 3. Concentration and Distribution as a set of

Exchanges as per Figure 3. We consider the

Distribution as a bundle (set) of Impacts of one

subject on several objects of nature, and the

Concentration as a bundle (set) of Appropriations of

several objects of nature by a subject.

The next elementary step in evolution is the

transition from singular to plural relations (a cluster

of exchanges).

These relations have forms of Concentration

and Distribution.

Fig. 3: Concentration and Distribution

Stage 4. Production is a network of all preceding

forms including interdependent Concentration -

Distributions as provided in Figure 4. The simplest

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

678

Volume 21, 2024

step in the transformation of Stage 3 is the evolution

from a single Distribution/ Concentration to

multiple interdependent Distributions/

Concentrations in which a set of subjects are in

relation with a set of objects.

Fig. 4: Production

Briefly, the stages of the evolution of pre-

economic relations and the corresponding pre-

control systems are presented in Table 1.

Table 1. Evolution of the concepts of PrER and their

equivalent concepts of pre-management systems

Pre-economic

relations

Pre-Management

System

Stage 1

Independent

Impact/

Appropriation

Accounting –

Transmitting

Stage 2

Exchange

Comparison of

Accounting/

Transmitting

Stage 3

Distribution/

Concentration

Search/ Choice

Stage 4

Production

Coordination of the

Search / Choice

network

3.3 Evolution of Pre-Economic Relations

into Economic Relations

Pre-economic relations evolve into economic

relations in the following way:

- When moving from the consideration of the

subject-nature relationship to the consideration of

the subject-subject relationship. At the same time, in

addition to the private nature of relations in pre-

economic relations, the social nature of relations

also arises. For management systems, it is

customary to talk about the emergence of

democratic management systems in addition to

authoritarian management systems.

It must be emphasized that in the evolution of pre-

economic relations, there is another intermediate

stage - this is the transition from relations in which

only natural tools are used to relations that include

tools produced with the help of other tools. The

appearance of artificial tools is a sign of a high level

of pre-economic relations, but not yet economic

ones.

Moving from subject-nature relations to subject-

subject relations, we get 4 types of relations, we call

them initial economic relations (IER).

The most important difference between economic

relations and pre-economic ones is that they (ER),

with the advent of the second subject, acquired the

opportunity to have both a private and public

character. As a result, four types of IER turn into an

exhaustive set of 16 evolutionary forms of economic

relations (ER).

We note the essential features of the

methodology for constructing the forms of evolution

of ER:

- each stage of IER development includes all

previous forms of IER as non-defining elements. It

should be noted that the previous stages also

contain, in a certain sense, more complex forms of

IER, namely, those in the form of causes for their

actual occurrence at subsequent stages (ER

developing contradictions [6], [9]).

- forms of PrER, “acquiring” the second subject and

turning into forms of ER, simultaneously get the

opportunity to acquire one of two properties, namely

the acquisition of either private or public nature of

relations between two economic entities. It is this

property that is the most important characteristic of

the basic elementary forms of ER evolution and it is

this property that gives rise to all 16 types of ER.

- for the Management Systems of Economic

Relations, this most important characteristic of ER

turns, respectively, into the authoritarian or

democratic nature of the management system.

It should be emphasized that this characteristic

of economic relations applies equally to both

entities involved. Thus, economic relations are

always of either private-private nature or public-

public nature.

- Each subject of ER is described by a set of four

IERs. Thus, we consider such relationships between

ER subjects as those where each subject is

represented by four IERs (that is, we consider the

subsets of relationship pairs). In other words,

because economic relations are intersubjective

relations, economic relations are introduced in the

form of pairs of such fours.

The main distinguishing feature of stages of the

economic relations evolution is their differences in

the set of characters (private or public) of the four

IERs that form each given type of ER (formation of

ER).

Likewise, the nature of the main primary forms

of management systems (public/private) is their

main distinguishing feature. It is this character

(public or private) that determines the authoritarian

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

679

Volume 21, 2024

or democratic forms of systems for managing

economic relations.

The law by which the transition from one quad-

characteristic feature to another takes place is the

dialectical law of withdrawal (negation of the

negation).

The process of changing stages is a stepwise

change in the form of economic relations when

independence is removed (the acquisition of a

public character) in a certain, higher type of IER

with the simultaneous restoration of the private

nature of one of the aspects of IER in the previous

form.

Thus, with the transition from stage to stage, the

dependence of the subjects moves to a higher and

higher level (Table 2), accumulating the social

nature of its aspects.

It should be noted that the transition from

studying the relationship between humans and

nature to considering the relationship as “a group of

people – a group of people” was carried out in two

steps. The first elementary step is the transition from

the study of human-nature relationships to the study

of relationships between people (person/person) for

the four types of IER.

The second elementary step is to assume that

one or both parties of the ER may also be the IER.

More precisely, economic relations are defined as

relations between IERs, with the clarification that

the operands in them can be both subjects and IERs.

That is, in the concept of economic relations we

also include relations between economic relations.

The most significant features of the real

evolutionary process of economic relations are

presented in Table 2, which contains the exhaustive

list of all possible evolutionary stages of economic

relations.

The most complete list of stages of ER

evolution includes 16 types of ER and, accordingly,

management systems of economic relations.

Moreover, each subject is described by the

entire four IERs, and each type of IER has a specific

character (Public or private).

By combining character values for each element

of the fours, we get a complete variety of sets of

private-authoritarian or public-democratic

characters of their relationships.

The theory of evolution of ER created in this

way defines a complete system of stages of

economic relations development both in the past and

present and future and, accordingly, defines all

possible types of management systems of economic

relations.

It can be assumed that the Economic Relations

of types 9, 11, 13 and 15 are expected to be stable,

but types 10, 12 and 14 are expected to be transient.

It is interesting to note that the System of absolutely

public economic relations and, therefore, the

corresponding Universally-Democratic Management

System are the economic interpretation of idea of a

purposeful-oriented system, [10].

Table 2. Evolutionary Stages of Economic Relations

(PR -private nature, SOC – public (social)

nature)

The important difference of the final stage of

economic relations evolution from all previous ones

is that the process of achieving the final

characteristics of all the elements of the quad (the

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

680

Volume 21, 2024

fully social nature of Economic Relations and,

accordingly, the fully democratic nature of the

Management System) is endless – it is the eternal

pursuit of the ideal.

It should be noted that for systems of Economic

Relations that are “private in nature” (PR), von

Neumann’s Theory of Game is applicable since the

private nature of ER means competition between the

parties.

For systems of Economic Relations that have a

“public (social) nature,” The Theory of Games is

inapplicable and must be improved since the social

nature means the cooperation of the parties

(common goals), and not the competition.

3.4 Stages of Evolution

It is generally recognized that the universal private

nature of economic relations and the authoritarian

form of their management were the most ancient,

[11].

However, at each stage of evolution, the private

nature of one of the aspects of IER is replaced by

the public one. The corresponding authoritarian

forms of economic relations management systems

are being replaced by more and more democratic

forms.

Note that the evolution of management systems

of ERs corresponds to the forms of ER evolution.

All four types of IER are contained in each type

of economic relationship. Thus, the type of ER is

described by four components, each of which can be

of a “private” or “public” nature.

The subsequent types of ER are contained in the

previous types in the form of undisclosed

contradiction, namely the contradiction associated

with the independence of subjects of economic

relations.

At each stage, one aspect of independence is

eliminated, acquiring the public character instead of

the private one.

The elimination of aspects of independence

continues until all the aspects of the independence

of the subjects of economic relations are eliminated.

Thus, the last stage of ER development is

characterized by the complete dependence of the

subjects.

In any society, it is easy to detect the

phenomena of almost any form of ER, from form 1

(family) to form 16 (commune).

The terms “stages” or “formations” are usually

used in the field of political economy, to denote the

forms given in Table 2.

3.5 An Example of the Development of

Rational Behavior of Subjects within a

Community

By the thesis that the utility of commodity A is not

its monetary value, but some measure depending on

its quantity, let us denote the utility of commodity A

as q(A) (the quantity of the commodity).

Each product A has a conversion vector into any

other product (in the multidimensional space of

goods), that is:

(1)

Then the utility of product A in terms of product B

will be:

(2)

Suppose that the community must decide which

of the subjects S1, S2, ... is more rational to transfer

product A from subject S0. This decision is made

based on a comparison of the utility of product B

produced by the subject Si, provided that he receives

product A. It should be taken into account that in

addition to product A, many other products were

used in the production of product B.

There are many levels of solving this issue,

depending on the depth of “prognostic” capabilities:

Level 1

Having received product A (the product being

sold), subjects can produce the following products:

Subject S1 - product B1, having spent the set of

products

(3)

...

Subject Sn- product Bn, having spent the set of

products

(4)

Then the comparable level 1 utility for the

community will be:

For product B1 – the utility is equal to:

(5)

...

For product Bn – the utility is equal to:

(6)

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

681

Volume 21, 2024

It would be rational to transfer product A to subject

S1 :

Sl: Ul = max (Ui, i {𝐼𝐵 1, 𝐼𝐵 2, … , 𝐼𝐵 𝑛} (7)

(maximization is carried out on products

produced with the use of product A. Product Bk is

produced using product A).

Carrying out similar reasoning for the purchased

product C in an exchange transaction and taking into

account the rationality of purchasing the product

that, during its production process “takes away” the

minimal utility from society, we find that rational

behavior would mean the receiving product C from

the subject:

Sm: Um = min (Uj, j{𝐽𝐷 1, 𝐽𝐷 2, … , 𝐽𝐷 𝑝}) (8)

Where 𝐽𝐷 1, 𝐽𝐷 2, … , 𝐽𝐷 𝑝- sets of products

necessary for the production of products D1, D2,

…, Dp.

(minimization is carried out for products that

are used in the production of product C. product

Dk are used in the production of product C).

Then the utility of the operation of exchanging

product A for product C will be:

UAC= Ul – Um (9)

Or in general form:

UAC = max(Ui - Uj), i {𝐼𝐵 1, 𝐼𝐵 2, … , 𝐼𝐵 𝑛}, j

{𝐽𝐷 1, 𝐽𝐷 2, … , 𝐽𝐷 𝑝} (10)

Level 2 (without a background, the option of

changing the history of the exchange of goods in the

past is not considered, i.e. the history of commodity

exchanges in the past cannot be changed).

Let us assume that from product Bl it will be

possible to obtain products:

(11)

and the utility of each of them is equal to:

(12)

which is calculated in the way as described above.

Accordingly, it would be rational to transfer

product Bl to subject p:

(13)

Then the second-order utility of transferring

product A to subject Sl will be:

(14)

Using the reasoning for the purchased

product C from level 1, the utility of the

operation of exchanging product A for product

C can be represented as:

UAC1,5 = Up2 – Um (15)

where Um is from (8) .

But such utility is not yet level 2, but level

“one and a half”, as it counts products produced

two levels down (produced with the use of

product A), but only 1 level up (used to produce

product C).

Having carried out similar to (8) reasoning

for purchased products that are used in the

process of production of products used to

produce product C in the exchange transaction,

and understanding the rationality for the society

of acquisition products that “remove” minimal

utility from the society, we can designate the

utility of the second level of exchange product

A for product C, as:

UAC2 = Up2 – Uk2 (16)

The above reasoning can be expressed in the

language of the theory of sets, more precisely in

the language of the Theory of Structures (N.

Bourbaki):

Let us introduce sets of subjects of

economic relations:

S = {Si} (17)

The set of objects (products) of economic

relations:

Ob = {Obi} (18)

The set of objects that are used in the

production of product i:

ObUpi = {ObUpi

j} j JU (19)

The set of objects for the production of which

product i is used:

ObDowni = {ObDowni

j} , j JD (20)

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

682

Volume 21, 2024

Then the “downward utility” of object (product)

i can be defined as:

UDowni = P(Obi X ObDowni) (21)

where P is the double Descartian or direct

multiplication of sets.

It's obvious that:

ObUpi = В({Obi}), and ObDowni В({Obi}),

where В(А) – Boolean of the set A (22)

The “upward utility” of object (product) i can

be defined as:

UUpi = P(Obi X ObUpi) (23)

“The utility of object (product)” i can be

defined as: Ui = P(UDowni X UUpi)

(24)

The utility of the ER “Exchange of object A for

C” of the first level can be defined as:

UАС = Р(UА Х UС ) (25)

The second level of utility is expressed as:

The “second level downward utility” of the

object (product) i can be defined as follows:

UDowni2 = P(ObiX{ObDownjk}), jJD (26)

The “upward utility” of object (product) i can

be defined as:

UUpi2 = P(Obi X {ObUpjk}) , j JU (27)

The “second level utility” of object (product) i

can be defined as:

Ui2 = P(UDowni2 X UUpi2) (28)

Similarly, we can construct the definition of

rational behavior of the 3rd level, in which we

formulate not only the utility of products produced

by using products produced by using product A, but

also of products produced by using products

produced by using products produced by using

product A ... The above arguments are carried out in

a similar way for all basic forms of economic

relations - not only for Exchange, but also for

Concentration/ Distribution and Production. If in

Exchange the relationship between two subjects is

considered, then in Concentration the relationship

“many subjects - one subject” is considered, and in

Distribution “one subject - many subjects”.

Accordingly, the next step of complexity leads to

the consideration of the relationship “many subjects

- many subjects,” which is the basic form of

Production.

4 Conclusions

Thus, the Theory of “rational” behavior of the

subjects (TRES) should include, in addition to the

Theory of Games, the theory designed to develop

decisions in conditions of the social nature of

economic relations. That is, in contrast to the

conditions when “each participant tries to maximize

a certain function (his profit), not all elements of

which are under his control”, [1], TRES should

describe the rational behavior of the subjects

seeking to maximize the “utility” for the entire

community.

In the transition from a private to a public

nature, the concept of “rational” behavior changes,

and, accordingly, the corresponding theory of

“rational behavior” changes. This transition adds

features of planning rather than a game to the theory

of rational behavior.

TRES for the public ER must solve two main

problems:

1. Determining the “usefulness” of product A for the

community, knowing its “usefulness” for each

subject of the community. By this utility, the

rational behavior of the subject of the community is

determined. The complexity of this task is

determined by two factors:

a. Utility is not the immanent property of product

A but depends on many factors – time,

geography, etc. A bottle of water on the shores of

Lake Ontario is not as useful as in the Sahara

Desert (which is not entirely true during the rainy

season).

b. The utility of product A for society must take

into account not only the utility of product A for

each of the subjects (UA(S)) but also the utility

for society of product B produced by a given

subject with the use of product A (UB(S)) (a kind

of weighting coefficient of the subject, which

also depends on time, place, etc.).

2. A method for finding the optimum in the problem

of enormous dimensions. When the community

consists of millions of subjects producing hundreds

of millions of goods, the purely computational task

of finding the optimum is not a simple matter.

3. In case when economic relations are at the public-

private stage, there are interacting communities

within which the public nature of economic activity

predominates, and the communities themselves act

on the external market with a private nature, TRES

retains all the main features of von Neumann’s

Theory of Games. With the clarification that the

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

683

Volume 21, 2024

usefulness of product A is determined not for an

individual entity, but for the entire community

interacting with another community. Similarly, for

product B received from another community, its

utility for the entire community receiving that

product must be determined.

4. In addition, the theory of evolution of economic

relations defines smaller stages of ER-associated

with the attribution of economic relations to four

basic forms: 1. Impact-Appropriation, 2. Exchange,

3. Distribution/Concentration, 4. Production.

It can be argued that the assignment of a given

economic relationship, for which rational behavior

is determined, to a specific element of these basic

forms will influence the determination of the

rational behavior of the subject participating in these

ERs. The specific form of ER (one of 16) plays a

decisive role in the distribution of the decision-

making process and in the choice of rational actions

of the actors involved.

5. Another aspect of the generalization of the

Theory of Games is the removal of the limitations of

the theory associated with the hypothesis introduced

by von Neumann about the role of money as a

universal "transferable numerical utility".

When studying the evolution of economic relations,

we consider money as performing only the

exchange function and, as noted in several works,

for example, [12], this function of money as a

means of exchanging goods and a means of

comparing the "utility" of goods loses its monopoly

and uniqueness as the property of global availability

of information and the property of global

availability of computing power for all participants

in economic relations are achieved.

Such global accessibility conditions mean the

availability of a complete report on current

commodity exchanges, taking into account all

regional and other circumstances.

Thus, the utility of the product in TRES must be

expressed not by means of money, but means of

pure numerical exchange rate of product A for any

other product B at any given region at any given

point of time.

6. The article presents the following new results:

- an approach to generalizing game theory is

proposed to expand the scope of its applicability

not only to economic relations based on

competition but also to economic relations based

on the cooperation of economic entities,

- an exhaustive classification of the forms of

economic relations covering the entire history

from the moment of the origin of economic

relations to the forms in the future, is proposed,

- the starting point of the development of

Economic Relations (human-human relations)

has been determined. Pre-economic Relations

(human-nature relations) present this starting

point,

- the principle of transformation of the initial pre-

economic relations into economic relations of

increasingly developed forms is indicated,

- the article indicates for what systems of

economic relations the classical game theory is

applicable, and for what ones it should be

improved,

- the "utility" indicator of goods for the community

of economic entities has been introduced. This

measure is not based on the concept of money,

but is based on the coefficients of exchange of

some goods for others ones and on the

interdependence of the utility (for society) of

goods in the technological chain of production,

- the mathematical analysis of the introduced

utility measure has been carried out.

References:

[1] Von Neumann, J., Morgenstern, O., Theory of

Games and Economic Behavior, Princeton

University Press, USA, 1953, p.641.

[2] Nash, J. Equilibrium points in n-person

games. Proceedings of the National Academy

of Sciences USA, 1950, 36, 48–49. Reprinted

in H. Kuhn (ed.), Classics in Game Theory,

Princeton University Press, Princeton, New

Jersey, 1997

[3] Maynard-Smith, J.; Price, G. R. The Logic of

Animal Conflict. Nature. 1973, #246 (5427):

15–18. doi:10.1038/246015a0.

[4] Marek Kruk , Piotr Artiemjew , Ewa Paturej,

The application of game theory-based

machine learning modelling to assess climate

variability effects on the sensitivity of lagoon

ecosystem parameters, Ecological

Informatics, Vol. 66, December 2021,

101462,

https://doi.org/10.1016/j.ecoinf.2021.101462.

[5] MAJ Nathan A. Lunde, The Use of Game

Theory at the Operational Level, A

Monograph by US Army School of Advanced

Military Studies US Army Command and

General Staff College Fort Leavenworth, KS,

USA, 2020, p.40.

[6] Shabarov, V., Ashikhmin, V., Basic

Principles of the Theory of Evolution of

Economic Relations Management Systems, in

Collection of materials of the 18th Congress

WOSC2021 “Systems approach and

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

684

Volume 21, 2024

cybernetics, directed to the future of

mankind”, 2021, p.54 – 63.

[7] Hegel, G. W. F., Science of Logic, Cambridge

University Press, UK, 2010, p.790.

[8] Pippin, Robert, Hegel’s Practical Philosophy:

Rational Agency as Ethical Life, Cambridge:

Cambridge University Press. 2012, p.308.

[9] Barrio, E.A., Da Ré, B.. Paraconsistency and

its philosophical interpretations, Australasian

Journal of Logic, 15 (2), 2018, pp.151–170.

[10] Ackoff, Russell L., Emery, Fred E., On

Purposeful Systems: An Interdisciplinary

Analysis of Individual and Social Behavior as

a System of Purposeful Events, Aldine-

Atherton: Chicago, 1972, ISBN-13: 978-

0202307985.

[11] Gregory K. Dow, Clyde G. Reed, Economic

Prehistory. Six Transitions That Shaped The

World. Cambridge University Press, 2023,

ISBN: 9781108878142.

[12] Davies, Glyn. A history of money from ancient

times to the present day, 3rd ed. Cardiff:

University of Wales Press, 2002. 720p. ISBN:

0708317170.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2024.21.56

Ashikhmin Victor, Shabarov Vladimir

E-ISSN: 2224-2899

685

Volume 21, 2024