Stability of Fuzzy Matrix Games for Conflicts: A Model with Uncertainty Preference Scheme

Abstract

Abstract In societal system disputes and in direct conflict of interests, in particular, the decision making faces a basic situation resembles a combat-like situation (Figure 1). For each of the opponents (‘players’) has in mind and carries out own missions in the societal environment (Figure 2) Furthermore, two or more parties need to make decisions with fully or partially conflicting objectives when involved in a dispute or open conflict. And yet, by and large, decisions must be made under risk, uncertainty, and incomplete or fuzzy information based on adaptive perception knowledge (Figure 3), which may imply large amounts of linguistic and probabilistic information with missing data. In the case of two opponents, the synergy of fuzzy approach and matrix games seems rather effective for modelling such multi-criteria conflicting situations. This synergy is feasible provide the game equilibrium stability concept is conceived in compliance with an adequate uncertainty preference scheme of decision making. In the case of two scenarios or states of a conflict, the preference scheme for a given participating decision-maker has to include components for handling cases of one state strict preference over another state, equal preference between the states, and also uncertainty preference. The fuzzy modelling based procedure is employed to take into account some of the subjective attitudes of the decision makers that are difficult to model using classical game theory.