АДАПТИВНА СКІНЧЕННА АПРОКСИМАЦІЯ НЕПЕРЕРВНИХ БЕЗКОАЛІЦІЙНИХ ІГОР

• Datum: 2020
• 1. Verfasser: Romanuke, V.V.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: неперервна безкоаліційна гра; одностороннє адміністрування; скінченна гра; дискретизація множини чистих стратегій; апроксимація розв’язків; переваги адміністратора
• Online Zugang: https://jais.net.ua/index.php/files/article/view/494
• Назва журналу: Problems of Control and Informatics

A problem of solving continuous noncooperative games is considered. It is presumed that a system modeled by a continuous noncooperative game can be administered from just one side eventually responsible for decisions in the system. Therefore, any solutions, regardless of how players treat them, should be studied and be in fact optimized only by the administrator. Thus, a procedure of adaptive finite approximation of continuous noncooperative games is presented, which is aimed at obtaining approximate solutions suitable for their practical implementation in systems with one-sided administering or control. The procedure consists of two stages. At the first stage, the players’ payoff functions are sampled by the uniform dichotomized breaking of the sets of their pure strategies. The respective finite noncooperative game is solved at the second stage. If its solution satisfies requirements of the administrator, then this solution is the result of the approximation. Otherwise, the procedure returns to the first stage, where the density of the breaking is twice increased and a new, «twice-complexified», game is solved. Such returns and complexifications are fulfilled until a solution of the corresponding finite game satisfies the administrator. Only the administrator decides which type of profitability, symmetry, or equilibrium is preferable, and whether the respective game solution is acceptable. The closeness of the approximate solution to the solution of the initial continuous game is not ascertained. The accuracy and quality of the approximation is treated in terms of how fast the finite game solution satisfies the administrator. A sequence of the already solved games is not removed, but serves as a basis for selecting the most rational solution considering operation speed, profitability, symmetry, and equilibrium.