Hypersoft game theory models and their applications in multi-criteria decision making

The classical game theory has been extended for soft set structures, and thus, soft game theory, fuzzy soft game theory, intuitionistic fuzzy soft game theory, neutrosophic soft game theory have been introduced. The payoff function in the soft game approaches is the set -valued function and allows the use of set operations to obtain solution, which makes it very convenient and easily applicable in practice. Also, in these game approaches, the strategies can be determined as attributes/parameters. That is, all these soft game theories are designed to manipulate parametric information using a single -attribute function. However, another powerful tool is needed to process parametric information obtained using multi -attribute function. To model such problems mathematically, the concept of hypersoft set has proposed. In this paper, a game theory model based on hypersoft set called hypersoft game theory is constructed. In this game theory, payoff function is the setvalued function and the strategies are chosen as multi -attributes. A twoperson hypersoft game is developed and different solution methods (such as hypersoft saddle point method, hypersoft elimination method, hypersoft Nash equilibrium method) are produced for such games. Also, the proposed methods are successfully applied to game theory -based decision making problems that may be encountered in real life. Finally, the two -person hypersoft game is extended to the n -person hypersoft game. Nash equilibrium of an n -person hypersoft game is described and an application for this solution method is presented.