Here are the steps to go through to find the determinant.

1. Pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row.
2. Multiply every element in that row or column by its cofactor and add. The result is the determinant.

The determinant of a matrix is a special number that can be calculated from a square matrix….To work out the determinant of a 3×3 matrix:

1. Multiply a by the determinant of the 2×2 matrix that is not in a’s row or column.
2. Likewise for b, and for c.
3. Sum them up, but remember the minus in front of the b.

In a matrix, the set of numbers are covered by two brackets whereas, in a determinant, the set of numbers are covered by two bars. The number of rows need not be equal to the number of columns in a matrix whereas, in a determinant, the number of rows should be equal to the number of columns.

The determinant of a square matrix is a single number that, among other things, can be related to the area or volume of a region. In particular, the determinant of a matrix reflects how the linear transformation associated with the matrix can scale or reflect objects.

A matrix is an array of many numbers. For a square matrix, i.e., a matrix with the same number of rows and columns, one can capture important information about the matrix in a just single number, called the determinant. The determinant of a 1×1 matrix is that number itself. …

Determinants can be calculated as the product of eigenvalues. Eigenvalues can be complex-valued. Note: I’m inclined to think they must be real because you can say that a determinant is just a generalized volume of a parallelotope made by the column vectors as the sides.

A matrix showing the pay-offs to each player in a two-player game. Usually the strategies available to the ‘row player’ are shown to the left of the matrix and the strategies available to the ‘column player’ are shown above the matrix. A pay-oflf matrix conforming to this description is shown below.

In the third stage of the 7th CPC pay matrix table (GP Rs. 2000), the pay scale level 3 is starting with the basic pay of Rs. 21700 and ends with Rs. 69100 with 40 annual increments.

Payoff Matrices. A payoff matrix is a way to express the result of players’ choices in a game. A payoff matrix does not express the structure of a game, such as if players take turns taking actions or a player has to make a choice without knowing what choice the other will make.

In game theory, a payoff matrix is a table in which strategies of one player are listed in rows and those of the other player in columns and the cells show payoffs to each player such that the payoff of the row player is listed first.

A payoff matrix is a visual representation of the possible outcomes of a strategic decision. A payoff matrix includes data for opponents, strategies, and outcomes. A payoff matrix can be used to calculate the aggregate outcome and to predict a strategy.

Payoff Matrix & Decision Rule. Payoff Matrix. The Payoff Matrix is an expression of the First Law of Decision Science. Each row represents one action that the decision maker might or might not freely choose to perform; Each column represents a possible state of nature.

Two commonly used decision-making tools are payoff matrices and decision trees. Payoff Matrices. A payoff matrix specifies the probable value of different alternatives, depending on different possible outcomes associated with each.

The simplest type of competitive situations are two-person, zero-sum games. These games involve only two players; they are called zero-sum games because one player wins whatever the other player loses.

A payoff is the outcome of a game that depends of the selected strategies of the players. Payoff = The value associated with a possible outcome of a game. Strategy = A rule or plan of action for playing a game. An optimal strategy is one that provides the best payoff for a player in a game.

Game Theory is Statistical Techniques applied in several Sectors. It provides the Arithmetic method game solving of , 2 X 2 ; n X n and its extension methods of Payoff matrix. KEYWORDS: conflicting, decision, dominance,payoff matrix, Saddle point,strategies.

Specifically, the solution methods and techniques discussed are Nash Equilibrium Method; Pareto Optimality Technique; Shapley Values Technique; Maximin-Minimax Method; Dominance Method; Arithmetic Method; Matrix Method; Graphical Method and Linear Programming Method.

Algebraic Method Example 1: Game Theory Two players, A & B, put down a coin. If coins match (i.e., both are heads or both are tails) A gets rewarded, otherwise B. However, matching on heads gives a double premium. Obtain the best strategies for both players and the value of the game.

First, we draw two parallel lines 1 unit distance apart and mark a scale on each. The two parallel lines represent strategies of player B. If player A selects strategy A1, player B can win 1 or -3 units depending on B’s selection of strategies.

To solve the matrix of game theory, graphical method is the easiest compared to other methods such as dominance property, matrix method etc. In the graphical method it is assumed that there is no saddle point.

Answer added by Clara Madu-Igwe. Payoff is one of the parts in every game theory.

As discussed in lecture material, game theory does in fact have limited practical applications in real life. The Ultimatum Game is a prime example of this. Game theory operates behind the assumption that players are “rational”, meaning that they strictly prefer larger payoffs than smaller payoffs.

Game theory is not a subject that is accessible to people without a rather strong math background. Not just calculus. You need to be very comfortable with probability and real analysis at a minimum. But even more pertinently, very few people who are not practicing economists have any real reason to study game theory.

Using game theory, real-world scenarios for such situations as pricing competition and product releases (and many more) can be laid out and their outcomes predicted. Scenarios include the prisoner’s dilemma and the dictator game among many others.