Game theory is defined as the science of strategy. In decision-making situations, individuals face conflictual and cooperative strategy methods against rational opponents in which different combinations of strategies result in different outcomes (Dixit, Nalebluff). Payouts differ depending on the type of game played, however they generally follow a trend that is 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 payouts and serve as rules for a particular game theory example. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay. A simple profit matrix to read is that of a two-person zero-sum game. In this payoff matrix, the trace of the matrix is ​​all zeros. The rest of the triangle is made up of one and one negative which represent a win or loss for one of the players. Furthermore, the rows and columns of the matrix contain the same elements in different order, so the zero vector is a linear combination of both the rows and the columns (Waner). Payoff matrices can be used to analyze phenomena such as dominant strategies. A strategy is dominant if, regardless of what the player chooses, the profit will be equal to or greater than any other available option given a given opponent's strategy. For example, suppose player 1 is given the choices (v1,…,vk) and player 2 is given the choices (w1,…,wn). If the payoff v1wn is equal to or better than any payoff vkwn, v1 is the dominant strategy of player 1. Likewise, if the payoff vkw1 is equal to or better than any payoff vkwn, w1 is the dominant strategy of player 2 (Sönmez) . There is also a phenomenon known as dominant strategy equilibrium where both players have a dominant strategy. In this case, it is very likely that both will choose their dominant option. This is the dominant strategy equilibrium. When a player has a dominant strategy, we can assume that he will choose the dominant option. In this case, the kxn payoff matrix will reduce in favor of the dominant actor. 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 iterated elimination of dominated strategies (Sönmez). If there are no profits resulting in this way, the strategies are non-dominant. A Nash equilibrium occurs when deviation from a given profit will always result in a smaller profit. This option is only present where there are no dominant strategies. In this case, for the Nash equilibrium vkwn, vk is the maximum profit in the vector v and wn is the maximum profit in the vector w (Sönmez). Profit matrices are also used to calculate what is known as 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. A pure strategy is when a player decides to play only one strategy. A strategy is completely mixed if all frequencies are greater than zero. The expected value e is found by multiplying the row frequency matrix, the column frequency matrix, and the profit matrix. The expected value represents the average profit per round given that players stick to their mixed strategies (Waner). The fairness of a game can be determined by its point.