Exploring dynamic equilibrium of alternatives on the base of rectangular stochastic matrices
Loading...
Date
2021
Authors
Oletsky, O.
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.
Description
Keywords
decision making, dynamic equilibrium, balanced rectangular stochastic matrices, Analytic Hierarchy Process, agents, conference materials
Citation
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.