It often results in sublevel grey full rank square matrix to become non-feasible solution square matrix when there are null-strategy variables and redundancy constraints in the grey matrix solving method of grey matrix game. We can not directly find the optimum grey game solutions in the non-feasible solution square matrix. However, we define concepts of nullstrategy variables and redundancy co...

This paper has two main goals: highlighting the connections between Stit logics and game theory and comparing Stit logics with Matrix Game Logic, a Dynamic Logic introduced by van Benthem order to model some interesting epistemic notions from game theory. Achieving the first goal will prove the flexibility of Stit logics and their applicability in the logical foundations of game theory, and wil...

The goal of this paper is to solve a matrix game with fuzzy payoffs. In this paper, a fuzzy matrix game has been considered and its solution methodology has been proposed. In this paper, fuzzy payoff values are assumed to be trapezoidal fuzzy numbers. Then the corresponding matrix game has been converted into crisp game using defuzzification of fuzzy number. Here, widely known signed distance m...

Replacing associated consistency in Hamiache’s axiom system by dual similar associated consistency, we axiomatize the Shapley value as the unique value verifying the inessential game property, continuity and dual similar associated consistency. Continuing the matrix analysis for Hamiache’s axiomatization of the Shapley value, we construct the dual similar associated game and introduce the dual ...

Game theory is not like the reinforcement learning which we have just talked about. In the game theory, the condition that one is playing against someone else is considered. Furthermore, game theory is not about learning, it does not learn from data or previous instances, but tries to figure out what to do given a specific game rule. A game could be described using a game matrix. The two player...