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By type of functions winning games are divided into: the matrix, bimatrix, continuous, convex, separable, such as duels, etc. Matrix game - this is the ultimate game of two players zero-sum, in which prizes are given by the first player in the form of a matrix (row corresponds to the number used first player's strategy, the column - the number of employed strategies of the second player, at the intersection of row and column of the matrix is winning the first player appropriate strategies applied). Winning the second player is the first defeat. For matrix games created quite a good theory and develop practical solutions acceptable methods. Thus, it is proved that any matrix game has a solution and it can easily be reduced to a linear programming problem and then solved using known techniques, such as the simplex method.

Bimatrix game - this is the ultimate game of two-player zero-sum, in which the winnings of each player are given by matrices separately for the respective players (in each matrix row corresponds to the first player's strategy, the column - a strategy the second player at the intersection of row and column in the first matrix is the first win player in the second matrix - winning the second player). For bimatrichiyh games also developed the theory of optimal behavior of players, but to solve such games is more complicated than usual matrix. Continuous is a game where the payoff function of each player is continuous, depending on the strategy (of course it is considered that the strategy expressed in numbers from a specific segment). Proved that games of this class have a solution "but not developed almost acceptable methods of finding them. A simple example of a continuous game of two players is as follows: The first player chooses a number x in the interval [0, 1 |, and the second player chooses a number from the interval [0, 11, after which the first player wins the x - y / 2, while the second loses only same.

Obviously the function x - Y2 is continuous and so the game is also considered to be continuous. According to the theorem of existence of solutions of this game has a solution. If the payoff function is convex, then this game is said to be convex. For which there are acceptable methods for the solution of finding the optimal pure strategy (a number) for one player and the probability of pure optimal strategies of other players. This problem can be solved relatively easily. If the payoff function can be represented as a sum of products of functions of one argument, then this game is called separable (separable). With the help of certain transformations of the solution is reduced to solving the game with bilinear payoff function and the definition of a fixed point for a special display of the sets of elements corresponding strategies. Games such as duels are characterized by the choice of the moment and the probability of obtaining prizes, depending on the time elapsed from the start of the game until the moment of choice. For example, there are interpretations of such games in the economic situation: each firm makes its capital contribution at a time to mastering the sales market. The sooner it will make a contribution, the less likely to master the market, but by making a contribution too late, it loses market. The payoff function of the players in games such as dueling takes a special kind: it is continuous for different values of the times when players make moves, and he "is discontinuous at the coincidence of the moments of the players. So there are no guarantees the existence of solutions for games such as duels. There are some methods for solving such games.