Game-Theoretic Model of the Species and Varietal Composition of Fruit Plantations

The horticultural industry is significantly influenced by climatic factors that cannot be accurately predicted. The aim of this study is to substantiate the species and varietal composition of plantations that provide maximum profit, taking into account the attractiveness of the variety and the influence of weather conditions on the results of management. Using the methods of game theory, analysis, and comparison, a game-theoretic model of the species and varietal composition of fruit plantations has been developed. The first matrix of the game contains “pure” strategies that consider only the placement of stone fruits of different ripening periods and “pure” strategies of nature that characterize the possible weather conditions affecting stone fruits. The second matrix of the game consists of “pure” strategies that consider the setting of only pome crops of different ripening periods and “clean” strategies that characterize possible weather conditions affecting the sowing of pome crops. On the basis of the processed material and the calculated indicators, the composition of groups of varieties of pome and stone fruit crops by ripeness for the enterprise is proposed. The results obtained show that the use of a theoretical and game model is effective for the development and selection of the best production solutions under conditions of uncertainty when the production process is highly dependent on random factors.

Game theory; Gardening; Model; Species and varietal composition; Strategy

At present, mathematical models are increasingly used in various disciplines, such as economics, medicine, and computer science. Also, many studies on mathematical models in the literature elicit scientific interest.

A developed mathematical model of factors driving product success not only examines specific products and scope but also uses a number of standardized success factors by building a mathematical model of the success factors that affect the success of various products (Setyaningrum et al., 2020).

Of interest is a mathematical modeling approach for optimal trade-offs in a wireless sensor network for a grain storage monitoring system (Onibonoje et al., 2019). Surya Admaja and Asvial (2021) proposed a modified routing model based on LEACH with distributing the cluster head to prevent adjacent cluster head from occurring.

Artificial neural networks, commonly referred to simply as neural networks, are one of them today, the most famous and, at the same time, mysterious means of data mining, which is developing thanks to achievements in the fields of neural network theory and computer science. Transforming seismic data into lateral sonic log properties was carried out successfully using the artificial neural network (Haris et al., 2018).

When developing a strategy under conditions of uncertainty, when random factors have a significant impact on the production process, it is recommended that game-theoretic models be used.

The horticultural industry is significantly influenced by climatic factors (random) that cannot be accurately predicted. At the same time, the most profitable crops suffer the most from the impact of negative weather factors. This situation significantly complicates the selection and justification of design solutions. In these tasks, it is advisable to use a game-theoretic model.

The purpose of the study is to substantiate the species and varietal composition of plantations, which maximize profits, taking into account the attractiveness of the variety and the influence of weather conditions on the results of management.

In game theory, the issues of finding the optimal behavior of participants in a conflict situation are considered. Participants, using certain strategies, strive to achieve maximum effects for themselves. Situation analysis boils down to choosing the best strategies for each participant and determining the amount of winnings. The gain can be a relatively higher efficiency in using resources, production assets, economic levers in production, and economic activities.

Of interest is the use of game theory algorithms for wireless sensor network optimization (Hendrarini et al., 2020). The use of game theory in economics makes it possible to obtain calculations to justify decision-making to improve efficiency (Allayarova et al., 2021). Game theory is used to solve real and current economic problems in different spheres of the economy. Therefore, a number of scientists have been engaged in developing the optimal strategy for the development of insurance business structures in a competitive environment (Yurynets et al., 2020). The designed game theory model allows the insurance company’s executives to determine the favorable insurance market conditions.

Of interest is the application of the theory of differential games in military affairs and economics (Korolyov, 2018). The article shows how the problem of differential economic-mathematical game arises from the simplest problems of classical variational calculus. Sufficient conditions for the Pontryagin Mangasarian maximum and their applications to the study of economic problems are investigated. Game theory and its optimum application for solving economic problems are discussed in Durmanov et al. (2019). However, this work does not reflect the peculiarities of the horticultural industry.

Agricultural production depends on a number of risks, such as soil, weather, climate conditions, seeds, price difference, organisms, and diseases. To reduce agricultural risks, the apparatus of game theory is used. Scientists researched the uppermost expected income of the lowest expected outcome earned from studying products in the worst conditions and the uppermost output in the lowest time with minimum investments (Kashid, 2017).

Tursunov et al. (2020) examined the question of for which products it is better to start the creation and development of small business in the agricultural sector (namely, growing vegetables) and what behavior helps reduce losses using the methods of game theory.

The problem of applying game theory for optimal cultivation of vegetables and fruits in the greenhouse is devoted to the work of Umarov et al. (2021). However, in this work, the optimal production structure was not presented, which would provide maximum profit.

In the study of Setyowati et al. (2021), choices of strategic alternatives are choices in determining which horticulture commodities will be grown: potato, cabbage, or scallion. However, this work did not reflect the peculiarities of the species and varietal composition of fruit plantations (Setyowati et al., 2021).

Summing up the study, we can formulate the following conclusions:

The horticulture industry is significantly influenced by climatic factors that cannot be accurately predicted. At the same time, the most profitable crops are bones of early and middle maturation, which are most affected by negative weather factors.

When developing a strategy in conditions of uncertainty when random causes have a significant impact on the production process, it is advisable to use a theoretical game model. The use of the theoretical and game model made it possible to determine the breed-grade composition of plantations, which ensures the maximization of profit, taking into account the attractiveness of the variety and the influence on the results of weather management.

Possible extensions for future research may include dynamic aspects or multi-objective functions.

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