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THE DECISION-MAKING PROCESS IN THE GAME ANTAGONISTIK'S
MATHEMATICAL MODEL
Mamatova Zilolaxon Xabibulloxonovna
Farg’mother state univer ofte's associate professor, pedagogical sciences
toe’citizens of philosophy doctor (PhD)
Orcid: 0009-0009-9247-3510
E-mail:
No'monova Qoriyaxon mo'sinjon kizi
Fergana state itniversiteti Applied mathematics - the direction of a
3-course students of the 22-09-the group of students
E-mail:
nomonovaqoriyaxon@gmail.com
Annotatsiya
: modeli asosida qaror qabul qilish strategiyasini tahlil qiladi ekologik xavfni
antagonistik o'yin o'yinlar moddaning nazariyasini kamaytirish jarayoni. Davlat va korxonalar
o'rtasidagi qarama-qarshi manfaatlarga erishish jadval, optimal strategiyalar va minimax
usullari bilan ifodalangan, shuningdek, sof maxi aniqlanadi. Egar nuqtasi borligi uchun nazorat
va atrof-muhit siyosati bo'yicha xulosalar va tavsiyalar ishlab chiqaradi qilindi. Tadqiqot
natijalari atrof-muhitda samarali qarorlar qabul qilishga xizmat qiladi.
Kalit so'zlar
: o'yin nazariyasi, o'yin antagonistik, ekologik xavf, optimal strategiya egar nuqtasi,
shuningdek qarang: maxi usuli, qaror qabul qilish, nol sumli o'yin, atrof-muhitni boshqarish,
strategik modellashtirish
Annotation:
the article analyzes the decision-making strategies based on the model of the
process in reducing environmental risks theo antagonistic game of the game. The table opposite
interests between the state and the achievement are expressed through the enterprise, and the
optimal strategies are determined by the minimax metho maxi visited and also on the net. The
existence of a point is investigated and conclusions and proposals for environmental policy are
seddl developer. The result of study to make effective decisions your object in the server
environment.
Keywords:
theo Game,Antagonistic game,environmental risks,the optimal strategy is not Seddl
point,see also: metho maxi,your decision-making Zero sum game,Environmental
management,strategic model
Annotasiya:
prinyatiya resheniy na osnove teorii v v igrovoy igrt strategy analiziruyutsya state
model is snijeniya ekologicheskogo prosess antagonisticheskoy matter the risk. Mejdu
gosudarstvom I cherez tablisu viigrishey predpriyatiem virajayutsya protivopolojnie the interior
of the optimal strategy are soon meto a matter chistie opredelyayutsya I minimaksa. I
ekologicheskoy I nalichie tochka seddla proveryaetsya virabativayutsya predlojeniya politik
vivod is po. Rezultati beginning prinyatiya resheniy effektivnix ekologicheskix slujat
issledovaniy.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
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page 1712
Klyuchevie
slovo:
igrt
any
theory,Antagonisticheskaya
igrt,Ekologicheskaya
opasnost,Optimalnaya strategy,Seddl tochka,other methods,Prinyatie resheniya,Igrt nulevoy s
roll,Ekologicheskiy management,modelirovanie Strategicheskoe
To enter .
The environmental problems of mankind today have become one of the most
pressing issues in the front. The unfolding activities of industrial enterprises as a result of
pollution, waste and the negative effects of harmful substances on the nature poses a threat to
environmental stability. In such a situation producers to reduce the environmental balance
between the state and the decisions on xavfni is born of a need to find. These decisions are
often a conflict of interest with both sides to achieve their goals and seeks was yesterday. This
mathematical game theory to the analysis of the context of the position the model will serve as
an effective means of antagonistik game. In this article the problem of two players to reduce
environmental xavfni — between public and modelling of industrial enterprises in the form of a
zero sum game. Through the identification of optimal strategies in environmental policy the
possibility to make effective and sustainable decisions are studied.
Literature analysis
Antagonistik o’optimal strategies in the yin to determine the presence of seddl point, as well as
strategies to limit the collection of birth and compact terms, Karush-kuhn-tucker (CC) have
been interpreted on the basis of the terms of. In this respect, whose basi T., “Dynamic
noncooperative game Theo” game and Owenning G. “Theo Game called” monograph plays a
particular role. The evolution of the development of this game in game theory, strategic
decision making in a changing environment, principles of linear and analytical form of charging
a zero sum game antagonistik has extensive coverage of the algorithm.
Research methodology
This research is based on game theory modelling of antagonistik xavfni reduce environmental
issue. Initially, the main government and industry as voters decide between entities o’strategic
zaro was to determine the relationship. Each one of them for complex decisions, constraints,
and profit/loss functions shakllantirildi. In the model, zero-yig’the indi game antagonistik the
use of structures, thus, each side strives own strategy to select the most comfortable.
For research, mathematical modeling and optimization methods — Lagrange multiplikator of
Simplex methods, the technique of identifying optimal solutions seddl point through the use of
led. The data collection process of the current environmental standards, is based on statistics
and monitoring of waste production.
The process of research — based on analysis of mathematical models of complex systems and
processes, effective management and distribution of resources aimed to determine the optimal
fandir of them. The various areas of this science — production, logistics, transport, planning
and economic system wide services are used. Making a decision, especially in conflict
situations in the modeling of strategic readers choice serves as the main means of the theory of
games.
Antagonistik game – this shows the reverse effect of the actions of the two opposite sides to
each other directly in the game. Choose from one of the available strategies to each side itself
and acts independent from the opposite direction.Antagonistik games for two player, zero sum
game. The benefits of a side in this game comes on two to lose. The results of the game
payments (advances) the expression of matrisa progressing through each player has joined the
biggest benefits to low most to lose or get. Maxi player and also visited the minimax approach
of using safe strategy, the value of is determined. The value of this is equal to you, then there
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
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will be the optimal solution for the game and it is seddl point. This theoretical approach allows
exact modeling of real processes and to make a decision. Research on environmental decisions
to reduce xavfni respects to the theory of games antagonistik model applied mathematical
modeling in the game. Two players — state and manufacturer directory — tries through the
selection of their strategies in the context of conflicting interests. Progress through it without
becoming a zero sum game schedule for each strategy was established and the model was
formed. Optimal strategies and minimax methods were used to determine the maxi also visited.
To check the availability of point seddl were found using the solution of the game in pure
strategies. As a practical example, the environmental condition of the vehicle xavfni rated based
on the efficiency evaluation was considered. Modeling is based on the results decide how
readers can analyze the formation of the movement.
Results and analysis
Xavfni research on reducing the environmental decision-making process were analyzed using
the model antagonistik game. The game has two sides — the state and the manufacturer
directory — the conflict between the interests of expression is directed. Based on the results of
the game is the payout schedule for each strategy. The strengthening of the environmental
strategies of the state penalties, tax rate increase, and the introduction of environmental
monitoring systems included. Their directory while environmental cleaning of the production
process, reduce waste or update existing technologies have the opportunity to choose strategies.
The theory of games Antagonistik — conflicting interests between these two sides on the basis
of the mathematical model is built, then each participant their maximum benefit, I will try to do
the minimum while the benefits of the opponent. These games are usually side is called a zero
sum game, because a win, lose the second hand exactly so.
On the basis of understanding how does it work?
This theory works on the basis of the following main concepts:
1. Participants (players) – each independent of the parties who accepted their decision.
2. Strategies – is a collection of choices that can be chosen for each participant.
3. Achievements (payment) function – the expectations of each participant for each pair of
strategies or loss of benefits.
4. The optimal strategy – how your opponent, let's try a strategy that gives the best results of the
participants.
5. Seddl point (a certain point) – the game changing strategies the participants in the collection
of glycogen matrisa the benefits of their strategy also change the point of useless.
6. Mixed strategy – a strategy with a certain probability by choosing multiple participants
determines their movement
Matrisa game model with antagonistik
The parties following strategies to make the payments (advances) is characterized by matritasi
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ISSN: 2692-5206, Impact Factor: 12,23
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Determine the availability of point Seddl
Payment matritasida seddl point of the game by determining the presence of or absence have a
solution in pure strategies is checked. You seddl point if there is a clear sign of the optimal
decision for the parties they could.
5. Mixed strategies solution methods and apply
If you seddl point is available, the optimal solution is found through the mixed strategies. At
this stage the following mathematical approach is applied:
* Simplex method
* Factor of lagrange
* Line in linear programming
Mixed strategies will identify by probability
Optimal value:
Analysis and interpretation of the results.In the final stage of the game will analyze the results.
Here is the level of environmental risk, economic loss or profit, and assessed the effects of
regulyator the effectiveness of environmental policy.
Statement of the issues
The authority of a city (A player) the following strategy against enterprises which produce
harmful waste in order to reduce environmental xavfnimay choose iya.
The cost of the strategies: from -10 to 10 pm, which is the value of winning here is regarded as
reduce the effectiveness of environmental xavfni. Power (A) how successful the move, the price
so high that, while successful enterprise in a show of resistance – this value is reduced.
State (A) strategies:
I1: Quick to conduct I1 – Quick inquiries (8 points)
I2: Fine held I2 – Fine application of (6 points)
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I3: temporarily stop the activity I3 – stop business (4 points)
Directory (player b) to protect himself while the following were chosen:
Directory (B) strategies:
J1: a legal claim to open J1 – the court of appeals (5 points)
J2: restore reputation through advertising J2 – mass advertising (3 points)
J3: J3 activity Hidden – Hidden activity (2 points)
Gameschedule:
J1(5)
J2(3)
J3(2)
I1(8)
8-5=3
8-3=5
8-2=6
I2(6)
6-5=1
6-3=3
6-2=4
I2(4)
4-5=-1
4-3=1
4-2=2
J1(5)
J2(3)
J3(2)
I1(8)
3
5
6
I2(6)
1
3
4
I2(4)
-1
1
2
A company for.
1-step. Each in a row, the minimum will find. Found results table to the right of the roof in the
refrigerator new in the column writes.
2-step . Most good of a strategy as a 1-step is found from the minimum to the maximum ,
corresponding to which row will select.
V the company for.
1-step. Each a column the maximum of finds. Found results table lower on the side of a new
line writes.
2-step . Most good of a strategy as a 1-step is found from the maximum to the minimum ,
corresponding to which the column will select.
In so doing, A company's own minimum achievements
to maximize try will (see also: maxi), same time
at V the company of their maximum lose that mini-
mallashtirishga move makes (minimax).
1)
I1: min(3,5,6)=3
I2: min(1,3,4)=1
I3: min(-1,1,3)=1
see also: max=max(3,1,1)=3
2)
J1 max(3.1 manuals,-1)=3
J2: max(5,3,1)=5
J3: max(6,4,2)=6
minmax=min(3,5,6)=3
Winning 3 points
A quick tekshuv
B to apply to the court
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ISSN: 2692-5206, Impact Factor: 12,23
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The final results.
So, antagonistik game model based on the maximum gains 3 points as a
result of analysis, the state — “A. Quick verification” Enterprise “to the court of appeal b.” they
come in a pair of strategies. This is a pair of strategies for the balance of the game and reflects
compliance with decisions aimed at reducing the environmental point xavfni make up.
Conclusion.
Environmental xavfni in this article, aimed at reducing the decision-making
process was studied based on the model antagonistik game. Conflicting interests between the
state and enterprises and their mathematical modeling is an analysis of the strategies and
achievements. Pure strategies in the modeling process can determine the point seddl on the
basis of a balanced solution. The decisions of voters as a result of research and decided that a
balance between providing optimal xavfni serves to reduce environmental strategies were
recommended. Effective protection of the environment can also be achieved through this
approach of showing economic was given.
The list of used literature:
1. 1. M. To'xtasinov. Jarayonlartadqiqoti. Textbooks. 2017. -572 b.
2. 2.M.
To'xtasinov.
Jarayonlartadqiqotidanmasalalarto'plami
(O'quvqo'llanma)-
"University".Tashkent - 2019. -206 b.
3. 3. In H. A. Tah. Operations research.-2010, 9 th Edition.
4. 4. By Mamadaliev N., M. Tuxtasinov. Variatsionhisobva optimal management
asosiymasalalari. Tashkent University. 2013. - 188.b.
5. 5. V.I.Biagodatskox. Optimal boshqaruvgakirish. Tashkent, 2019, -248 b.
6. M. To'xtasinov. The process of research. Textbooks. 2017. -572 b.
7. 6. “I Am The Travel Of Your Sales Problem: A Computational Study” — D. L. Applegate,
R. E. Bixby, V. Chvatal, W. J. Cookie.
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