Game-Theoretic Model of the Optimal Distribution of Labor Resources

The article presents a model of the optimal distribution of labor resources. The developed game-theoretic model of a static optimal-purpose problem is described as a game in normal form. In the game, many workers and many enterprises are given, and the situation is a substitution. Each substitution is one of the possible assignments of workers to enterprises. An assessment criterion has been introduced to select an employee or enterprise. The number of the assessment criterion is called the utility for the employee from being assigned to the enterprise (degree of satisfaction of the interests of the player), and for the enterprise - the utility for the enterprise from appointing an employee to him (degree of satisfaction of the interests of the player). From the numbers of the evaluation criterion, the utility matrices are written and the matrix of winnings of the players in the game is constructed. The matrix is used to construct a compromise set in the game and find a compromise gain, which is the guaranteed gain of the least satisfied player. An algorithm for constructing a compromise set is presented in steps. For the algorithm, its temporal estimate and complexity class are found. Thus, the article presents a solution to the static problem of the optimal distribution of labor resources based on the principle of optimality of a compromise set.