Game-Theoretic Model of the Dynamic Problem of Labor Resources Optimal Assignment

The paper considers a game-theoretic model of a dynamic optimal-purpose problem using the example of the labor market functioning. A deterministic model of the workers optimal distribution among enterprises is described taking into account changing conditions over a period of time. At each moment of time, the state of the employee and the enterprise are determined. Moments of time are moments of the system stationary states. In each stationary state, a game in normal form is determined. In the game there is a compromise situation, optimal policy, and the system's income from appointments is calculated as the sum of the payoff functions of all players. The functioning of the labor market as a system for some periods of time is presented as a multi-step game on a tree. In a one-step game based on the principle of compromise set optimality, there is a compromise situation and the corresponding compromise control vector. On the multi-step game tree, there is a compromise income of the system in a few steps, when a sequence of games was realized, and a compromise path corresponding to a sequence of compromise control vectors. The compromise system income and the sequence of compromise controls are found using dynamic programming recurrence relationships. Thus, it is possible to indicate the optimal behavior of all participants in the labor market at any given time.

I. Introduction

In the work, on the example of the labor market functioning, a game-theoretic model of the dynamic problem of labor resources optimal assignment is considered. A deterministic model of the workers optimal distribution is described. by enterprises subject to changing conditions over time periods. At every moment in time defined many socio-economic conditions of the employee , and financial and economic conditions of the enterprise . The state vectors of workers and enterprises define the state vector of the labor market, or system, at time , where is many states of the system at time is a status number. Moments of time are moments of stationary states of the system. In each stationary state normal play defined . In the game a compromise situation found , optimal labor exchange policy , and also calculated the system revenue from appointments as the sum of all players payoff functions. The compromise system revenue and the sequence of compromise controls are found using the dynamic programming recurrence relations [1]–[4].