UDC 004.82.855'24
1 National University of "Kyiv-Mohyla Academy," Kyiv, Ukraine
 oletsky@ukr.net
|
|
FORMALIZING THE PROCEDURE FOR THE FORMATION OF A DYNAMIC EQUILIBRIUM
OF ALTERNATIVES IN A MULTI-AGENT ENVIRONMENT IN DECISION-MAKING
BY MAJORITY OF VOTES
Abstract. In order to investigate individual and collective behavior of agents, the model called the "state-probability of choice"
has been suggested. The model is based on implicit regarding of choice probabilities and on the Markov chain of changing these probabilities.
The main point of the model is a "state-probability of choice" matrix whose rows correspond to states and the columns correspond to alternatives.
Within this model, some sufficient conditions of the dynamic equilibrium between two alternatives have been established.
The dynamic equilibrium means that different alternatives are being chosen by rotation, and any of them has no advantage over others.
The way of forming "state-probability of choice" matrices providing the dynamic equiibrium has been suggested.
Keywords: decision-making situation, dynamic equilibrium, agents.
FULL TEXT
REFERENCES
- Russell S., Norvig P. Artificial Intelligence: A Modern Approach [Russian translation]. Moscow: Publishing house. house "Williams", 2006. 408 p.
- Nikolenko S.I., Tulupyev A.L. Self-learning systems [in Russian]. Moscow: MCNMO, 2009. 288 p.
- Letichevsky A.A. Algebraic theory of interaction and cyber-physical systems. Problemy upravleniya i informatiki. 2017. N 5. P.37тАУ55.
- Tarasov V.B. From multi-agent systems to intelligent organizations [in Russian]. Moscow: Editorial URSS, 2002. 352 p.
- Moulin E. Cooperative decision making. Axioms and models [Russian translation]. Moscow: Mir, 1991. 464 p.
- Mashchenko S.O. A mathematical programming problem with the fuzzy set of indices of constraints. Cybernetics and systems analysis. 2013. Vol. 49, N 1. P. 62тАУ68. https://doi.org/10.1007/ s10559-013-9485-4.
- Oletsky O.V. On the approach to modeling the decision-making process in a multi-agent environment based on the Markov process of changing the probabilities of choice. Scientific notes of NaUKMA. Computer Science. 2018. Vol. 1. P. 40тАУ43.
- Horn R., Johnson C. Matrix Analysis [Russian translation]. Moscow: Mir, 1989. 655 p.
- Saati T. Decision Making. Hierarchy analysis method [Russian translation]. Moscow: Radio i svyaz', 1993. 278 p.
- Chernorutskiy I.G. Decision making methods [in Russian]. St. Petersburg: BHV-Petersburg, 2005. 416 p.
- Hlybovets M.M., Oletsky O.V. Artificial Intelligence [in Ukrainian]. Kyiv: Vydavnychyy dim ┬лAkademiya┬╗, 2002. 366 p.
- Ivokhin E.V., Apanasenko D.V. Clustering of composite fuzzy numbers aggregate based on sets of scalar and vector levels. Journal of Automation and Information Sciences. 2018. Vol. 50, N 10. P. 47тАУ59. https://doi.org/10.1615/jautomatinfscien.v50.i10.40.
- Provotar O.I., Provotar O.O. Fuzzy probabilities of fuzzy events. Kibernetika i sistemnyj analiz. 2020. Vol. 56, N 2. P. 3тАУ13.
