Game theory is defined as the science of strategy. In decision-making situations, individuals face conflicting and cooperative methods of strategy against rational adversaries in which different combinations of strategies result in different payoffs (Dixit, Nalebluff). Payouts differ depending on the type of game played, however, they generally trend positive for both players, negative for both players, or positive for one and negative for the other. Matrices are constructed to calculate and present these different payoffs and serve as rules for a particular case of game theory. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get an original essay A simple to read payoff matrix is ​​one of the zero-sum games for two people. In this payoff matrix, the trace of the matrix is ​​composed entirely of zeros. The rest of the triangle is made up of ones and negatives which represent a win or loss for one of the players. Additionally, the rows and columns of the matrix contain the same elements in a different order, so the zero vector is a linear combination of the rows and columns (Waner). Payoff matrices can be used to analyze phenomena such as dominant strategies. A strategy is dominant if, whatever the player's choice, the payoff will be equal to or greater than any other available option given a certain opponent's strategy. For example, let's say player 1 has choices (v1,…,vk) and player 2 has choices (w1,…,wn). If payoff v1wn is equal to or greater than any payoff vkwn, v1 is player 1's dominant strategy. Similarly, if payoff vkw1 is equal to or greater than any payoff vkwn, w1 is player 1's dominant strategy. player 2 (Sönmez). There is also a phenomenon known as dominant strategy equilibrium in which both players have a dominant strategy. In this case, it is very likely that they will both choose their dominant option. This is the dominant strategic balance. When a player has a dominant strategy, it can be assumed that he will choose the dominant option. In this case, the kxn matrix of payoffs will decrease in favor of the dominant player. Therefore, if player 1 has the dominant strategy but player 2 does not, the original kxn choice matrix is ​​transformed into a 1xn matrix with the assumption that player 1 will choose only the dominant strategy. This is called iterative elimination of dominated strategies (Sönmez). If no gains result in this manner, the strategies are non-dominant. A Nash equilibrium occurs when deviating from a given payoff will always result in a smaller payoff. This option is only present in the absence of dominant strategies. In this case, for the Nash equilibrium vkwn, vk is the largest payoff in vector v and wn is the largest payoff in vector w (Sönmez). Payoff matrices are also used to calculate what is called an expected value. Expected values ​​can be found when players decide to use mixed or pure strategies. A mixed strategy is when a player decides to play their strategies at predetermined frequencies. Pure strategy is when a player decides to play only one strategy. A strategy is fully mixed if all frequencies are greater than zero. The expected value e is found by multiplying the row frequency matrix, column frequency matrix and gain matrix. The expected value represents the average win per round given that players stick to their mixed (Waner) strategies. The fairness of a game can be.