The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

In this paper, we consider an interval matrix game with interval valued payoffs, which is the generation of the traditional matrix game. The “saddle-points”of this interval matrix game are defined and characterized as equilibrium points of corresponding non-zero sum parametric games. Numerical examples are given to illustrate our idea. These results are extended to the fuzzy matrix games. Also,...

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players’ strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any co...

Matrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective linear programming method for solving matrix games in which the payoffs are expressed with intervals. Because the payoffs of the matrix game are intervals, the value of the matrix game is an interval as well. Based on the...

Much of the commercial success that Enter The Matrix has enjoyed is the result of its relationship with the Matrix trilogy, rather than the quality of play it offers. The game was released at the same time as The Matrix Reloaded (May 2003) and immediately became the fastest-selling title in its publisher’s history. The game is part of the Matrix franchise, but whatever its allegiances, it is a ...

2.1.1 matrix games A 2-player zero-sum game, or a matrix game, is defined by a matrix A ∈ Rm×n, called the payoff matrix. There are two players with opposing interests: the row player (minimizer) and the column player (maximizer). At each step of the play, the row player selects a row i, and the column player selects a column j, then the row player pays to the column player the value aij of the...

A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players. By this formulism, a new way to find the equilibria of games is given by generalizing the thermodynamical evolutionary process leading to equilibrium in Sta...

A zero-one matrix A contains another zero-one matrix P if some submatrix of A can be transformed to P by changing some ones to zeros. A avoids P if A does not contain P. The Pattern Avoidance Game is played by two players. Starting with an all-zero matrix, two players take turns changing zeros to ones while keeping A avoiding P. We study the strategies of this game for some patterns P. We also ...

A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix gives the payoff of players. By this formalism, a new way to find the equilibria of games is given by generalizing the thermodynamical evolutionary process leading to equilibrium in St...