An equilibrium in group decision and its association with the Nash equilibrium in game theory

Abstract

An equilibrium for group decision is introduced, and its association with the Nash equilibrium in game theory is examined. The experts’ preferences in the group decision situation are assumed to be ties-permitted ordinal rankings and represented by preference sequence vectors (PSVs). In particular, this paper is concerned with: (1) the introduction of a group decision equilibrium which is described by using PSVs; (2) the description of the Nash equilibrium by using PSVs; (3) the approach for calculating the Nash equilibrium by means of PSVs; (4) the comparison of the introduced PSV approach and an existing method for calculating the Nash equilibria; and (5) the relationship of the group decision equilibrium in group decision making and the Nash equilibrium in game theory. The observations are helpful for perceiving the relationship between the group decision making and the game theory.