Exploring dynamic equilibrium of alternatives on the base of rectangular stochastic matrices

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Oletsky, O.
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A problem of individual and collective decision making and choosing between some alternatives is regarded. Within this context, dynamic equilibrium between alternatives, which means that no alternative has advantages over the others, is explored. We are developing an approach on the base of matrices, rows of which correspond to various distributions of importance among alternatives. Such matrices are called balanced rectangular stochastic matrices. We suggest that the Analytic Hierarchy Process (AHP) should be applied for getting matrices of importance. From such a matrix we can move on to a matrix which represents probabilities of choosing each alternative. The proposed model involves some parameters, one of which affects the spread of importance values between the best and the worst alternatives, and the other one reflects a degree of an agent’s decisiveness. A Markov chain is used for modeling possible changes of agents’ preferences. Some experiments illustrating the situation of dynamic equilibrium have been carried out and are reported in the paper. Possible ways of breaking such a situation, namely by changing transition probabilities and by changing agents’ decisiveness, are described. If a decision is made by a group of agents, which is big enough, a slight advantage of one alternative over the other may ensure steady wins for this alternative. For agents of influence who are trying to shift a situation from the point of a dynamic equilibrium by means of affecting what agents know or how they behave, possible strategies are discussed. Models describing such influences may involve Markov decision processes and a game-based approach.
decision making, dynamic equilibrium, balanced rectangular stochastic matrices, Analytic Hierarchy Process, agents, conference materials
Oletsky O. V. Exploring dynamic equilibrium of alternatives on the base of rectangular stochastic matrices / O. V. Oletsky // 3rd International Workshop on Modern Machine Learning Technologies and Data Science Workshop, MoMLeT and DS 2021, Lviv-Shatsk, 5 June 2021 - 6 June 2021, 170615. - 2021. - Vol. 2917. - P. 151-160.