New expected impact functions and algorithms for modeling games under soft sets

Abstract

Soft set is the power tool to deal with uncertainty in a parametric manner. In applications of soft set, one of the most important steps is to define mappings on soft sets. In this study, we model theory of game under theory of soft set which is an effective tool for handling uncertainties events and problems that may exist in a game. To this end, we first define some expected impact functions of players in soft games. Then, we propose three new decision making algorithms to solve the 2.2 × p, 2 . n × p and m . 2 × p soft matrix games, which cannot be settled by the relevant soft methods such as saddle points, lover and upper values, dominated strategies and Nash equilibrium. The proposed soft game algorithms are illustrated by examples.