Optimizing the strategy of activities using numerical methods for determining equilibrium

Abstract

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