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

To analyze agents’ individual and cooperative behavior, a “state–probability of choice” model is proposed. It is based on an explicit consideration of the probabilities of choosing alternatives and on the Markov chain of variation of these probabilities. The model’s central place is the “state–probability of choice” matrix, whose rows correspond to states and columns correspond to alternatives. Within the framework of this model, sufficient conditions for the dynamic equilibrium of two alternatives are established if a simple majority of votes make decisions. Dynamic equilibrium means that different alternatives are chosen in turn, and with multiple choices, each of them has no priority over the others. We obtained a constructive method for forming “state–probability of choice” matrices, for which the dynamic equilibrium of alternatives is provided.