Competitive prediction in case of defective probability distribution

Competitive prediction of random variable, which could have defective distribution is considered. The scale of prediction accuracy representing monotonically decreasing continuous function is presented. The size of players reward is determined as difference of predictions values measured in a built scale. It is shown, that in case of natural assumption implementation the scale of accuracy of prediction represents a function that is proportional to the distribution function of random variable. The game for two players for two different options is formulated. As a result of change of variables the game defines on the units square with continuous payoff function. The sets of the players strategies represent the segments of unit length. In the case of zero-sum game the optimal players strategies in mixed strategies are found and the uniqueness of found equilibrium is proved for a type of mixed strategies with carrier containing two points. In the case of non-zero-sum-game two equilibriums are found in clear strategies. Bibliogr. 5.