Economic-mathematical modeling of employment contracts at the recruitment procedure

The paper considers an economic-mathematical model of the recruitment procedure. In the real sector of economy, employers are often incapable of evaluating professional skills of a candidate for a certain job position. This problem is becoming more pressing nowadays, when managers are usually proficient in managing skills but do not have a relevant job experience. Under these conditions, a specialist from among the employees could be better at assessing qualities of a candidate from outside the company. Thus, the principal (a firm owner/manager) may wish to use his employees' knowledge to hire new smart (skilled, talented) staff. However, workers know that the firm will only keep a limited number of workplaces. That may be for various reasons: perhaps, in a division inside a big company there is a quota on the number of workplaces; or the firm needs a limited number of qualified employees to produce its optimal output. Thus, workers have incentives to prevent more talented candidates from getting a job because those people may later recommend the principal to replace less gifted ones. In the paper, we consider this conflict using the modeling approach of game theory. The research appears to be currently relevant since there is a necessity to solve personnel problems at all levels, including the level of the firm's activity. The novelty of the solution to this task in Russian scientific literature is provided by the solution method and the essential content - application of the game theory to decision-making problems in the contract theory. Unlike foreign analogs, the problem of delegation of powers is considered as a solution to the task on social optimum, when the profitability of the company reaches the maximum but the amount of payment to workers does not decrease. It is shown that to achieve the social optimum the owner has to delegate powers to competent employees.