Optimizing the strategy of activities using numerical methods for determining equilibrium

The paper considers issues on the theoretical substantiation of options for choosing an optimal strategy to integrate an agricultural enterprise into the wholesale market by using methodological tools of the non-cooperative game theory. We have proposed modeling the behavior of an agrarian enterpris...

Full description

Bibliographic Details
Main Authors: Iryna Sievidova, Tamila Oliynik, Oleksandra Mandych, Tetyana Kvyatko, Iryna Romaniuk, Larisa Leshchenko, Serhiy Vynohradenko, Serhii Plyhun
Format: Article
Language:English
Published: PC Technology Center 2019-12-01
Series:Eastern-European Journal of Enterprise Technologies
Subjects:
Online Access:http://journals.uran.ua/eejet/article/view/187844
id doaj-516b6df30dc64ef6ae406207b3faf45b
record_format Article
spelling doaj-516b6df30dc64ef6ae406207b3faf45b2020-11-25T02:19:34ZengPC Technology CenterEastern-European Journal of Enterprise Technologies1729-37741729-40612019-12-0164 (102)475610.15587/1729-4061.2019.187844187844Optimizing the strategy of activities using numerical methods for determining equilibriumIryna Sievidova0Tamila Oliynik1Oleksandra Mandych2Tetyana Kvyatko3Iryna Romaniuk4Larisa Leshchenko5Serhiy Vynohradenko6Serhii Plyhun7Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002Kharkiv National Agrarian University named after V. V. Dokuchaiev p/o “Dokuchaevske-2”, Kharkiv dist., Kharkiv reg., Ukraine, 62483Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002Kharkiv Petro Vasylenko National Technical University of Agriculture Alchevskykh str., 44, Kharkiv, Ukraine, 61002Kharkiv National Agrarian University named after V. V. Dokuchaiev p/o “Dokuchaevske-2”, Kharkiv dist., Kharkiv reg., Ukraine, 62483Kharkiv National Agrarian University named after V. V. Dokuchaiev p/o “Dokuchaevske-2”, Kharkiv dist., Kharkiv reg., Ukraine, 62483Kharkiv National Agrarian University named after V. V. Dokuchaiev p/o “Dokuchaevske-2”, Kharkiv dist., Kharkiv reg., Ukraine, 62483The paper considers issues on the theoretical substantiation of options for choosing an optimal strategy to integrate an agricultural enterprise into the wholesale market by using methodological tools of the non-cooperative game theory. We have proposed modeling the behavior of an agrarian enterprise in the market by achieving a Nash equilibrium under various scenarios of competitors’ activities and volumes of information on market conditions. The methodology has been substantiated to apply the iterative algorithms to calculate equilibria in a general class of non-quadratic convex polyhedra in order to form the methodologies and construct algorithms for a behavior of agricultural enterprises in market activity. It was determined that decision-making occurs in parallel to the real conditions of activity of an agricultural enterprise in the wholesale market. The comprehensive application of numerical methods based on solving the optimization problems provides a smooth approach to the Nash equilibrium. A game can have multiple isolated Nash equilibria if players have non-quadratic payment functions when solving such problems. Based on the above, the results were determined of local convergence, since global results have strong constraints in non-quadratic problems. However, there is a connection with semi-global practical asymptotic stability if players have quadratic payoff functions. It has been shown that there is a shift in the convergence in proportion to the amplitudes of disturbance signals and the third derivative of payoff functions for non-quadratic payoff functions. This shift in the convergence corresponds to the shift in a numerical example. It has been determined that the learning strategy developed in accordance with the main provisions of the theory of games remains attractive if one has partial information on the state of the market. Application of the indicated action strategy provides a company with a possibility to improve its initial position by measuring its own payoff values only and not using estimates of potentially uncertain parameters. It has been proposed to use applied tools from the game theory to determine an optimal action strategy for an agricultural enterprise for its integration into the wholesale market of vegetable productshttp://journals.uran.ua/eejet/article/view/187844game theoryaction strategyagricultural enterprisewholesale marketnash equilibrium
collection DOAJ
language English
format Article
sources DOAJ
author Iryna Sievidova
Tamila Oliynik
Oleksandra Mandych
Tetyana Kvyatko
Iryna Romaniuk
Larisa Leshchenko
Serhiy Vynohradenko
Serhii Plyhun
spellingShingle Iryna Sievidova
Tamila Oliynik
Oleksandra Mandych
Tetyana Kvyatko
Iryna Romaniuk
Larisa Leshchenko
Serhiy Vynohradenko
Serhii Plyhun
Optimizing the strategy of activities using numerical methods for determining equilibrium
Eastern-European Journal of Enterprise Technologies
game theory
action strategy
agricultural enterprise
wholesale market
nash equilibrium
author_facet Iryna Sievidova
Tamila Oliynik
Oleksandra Mandych
Tetyana Kvyatko
Iryna Romaniuk
Larisa Leshchenko
Serhiy Vynohradenko
Serhii Plyhun
author_sort Iryna Sievidova
title Optimizing the strategy of activities using numerical methods for determining equilibrium
title_short Optimizing the strategy of activities using numerical methods for determining equilibrium
title_full Optimizing the strategy of activities using numerical methods for determining equilibrium
title_fullStr Optimizing the strategy of activities using numerical methods for determining equilibrium
title_full_unstemmed Optimizing the strategy of activities using numerical methods for determining equilibrium
title_sort optimizing the strategy of activities using numerical methods for determining equilibrium
publisher PC Technology Center
series Eastern-European Journal of Enterprise Technologies
issn 1729-3774
1729-4061
publishDate 2019-12-01
description The paper considers issues on the theoretical substantiation of options for choosing an optimal strategy to integrate an agricultural enterprise into the wholesale market by using methodological tools of the non-cooperative game theory. We have proposed modeling the behavior of an agrarian enterprise in the market by achieving a Nash equilibrium under various scenarios of competitors’ activities and volumes of information on market conditions. The methodology has been substantiated to apply the iterative algorithms to calculate equilibria in a general class of non-quadratic convex polyhedra in order to form the methodologies and construct algorithms for a behavior of agricultural enterprises in market activity. It was determined that decision-making occurs in parallel to the real conditions of activity of an agricultural enterprise in the wholesale market. The comprehensive application of numerical methods based on solving the optimization problems provides a smooth approach to the Nash equilibrium. A game can have multiple isolated Nash equilibria if players have non-quadratic payment functions when solving such problems. Based on the above, the results were determined of local convergence, since global results have strong constraints in non-quadratic problems. However, there is a connection with semi-global practical asymptotic stability if players have quadratic payoff functions. It has been shown that there is a shift in the convergence in proportion to the amplitudes of disturbance signals and the third derivative of payoff functions for non-quadratic payoff functions. This shift in the convergence corresponds to the shift in a numerical example. It has been determined that the learning strategy developed in accordance with the main provisions of the theory of games remains attractive if one has partial information on the state of the market. Application of the indicated action strategy provides a company with a possibility to improve its initial position by measuring its own payoff values only and not using estimates of potentially uncertain parameters. It has been proposed to use applied tools from the game theory to determine an optimal action strategy for an agricultural enterprise for its integration into the wholesale market of vegetable products
topic game theory
action strategy
agricultural enterprise
wholesale market
nash equilibrium
url http://journals.uran.ua/eejet/article/view/187844
work_keys_str_mv AT irynasievidova optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT tamilaoliynik optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT oleksandramandych optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT tetyanakvyatko optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT irynaromaniuk optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT larisaleshchenko optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT serhiyvynohradenko optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
AT serhiiplyhun optimizingthestrategyofactivitiesusingnumericalmethodsfordeterminingequilibrium
_version_ 1724875959866228736