#### Abstract

The purpose of this paper is to study optimal relationships between customer, main contractor, and subcontractor. We make the following assumptions: main contractor and subcontractor have types that specify expenses and outcomes for all actions that can be performed. The higher type has fewer expenses for the same action, and optimal action increases with type. Contractors announce their types but can cheat, i.e., not reveal true types. The action and the respective remuneration are specified by the higher authority accordingly to the type declared. Incentives are paid so distorting real type is disadvantageous both for main contractor and subcontractor. We consider these assumptions to be compatible with economic practice. Methodology. We apply methods of contract theory, probability theory, and variation calculus, appropriately modifying apparatus of classic basic incentive problem. Variety of types of (sub-)contractors available is described via probability distributions. Then expected values of profits for participants are calculated as integral functionals. Maximization of these functional results in implicit equations for optimal incentive functions. Results. A method for optimization of activity of all participants is developed. Its requirements are traditional and non-restrictive; hence the expected area of applications is wide enough. Optimal actions and incentive functions are found. Formulae for the influence of expected main contractor and subcontractor’s productivity and expenses on customers profit and payoffs are presented. Conclusions. It is shown that generally customer does not need to collect information about real subcontractor, relying on main contractor, but should take into account the actual situation in the respective branch. In the case when the customer is fully informed about this situation, contractor’s expected profit does not depend on subcontractor’s type (although it is only a mathematical expectation and a concrete result can vary).

#### Keywords

contract theory, principal, agent, incentive compatibility, main contractor, subcontractor

#### References

Blahun I., Dmytryshyn L. & Leshuk H. (2017). Simulative model for evaluation of investment processes in the regions of Ukraine. Investment Management and Financial Innovations, 14(3), 322-329.

Bolton P. & Dewatripon M. (2005). Contract Theory – Cambridge, Mass & London, England: MIT Press.

Cabrales A. & Charness G. (2000). Optimal Contracts, Adverse Selection and Social Preferences: An Experiment. Economics Working Papers 478, Department of Economics and Business, Universitat Pompeu Fabra.

Grossman S. & Hart O. (1982). Implicit Contracts Under Asymmetric Information. Quarterly Journal of Economics, 1, 110-124.

Grossman S. & Hart O. (1983). An Analysis of the Principal-Agent Problem. Econometrica, 51(1), 7-45.

Laffont J.-J. & Martimort D. (2002). The Theory of Incentives. The Principal – Agent Model – Princeton & Oxford: Princeton University Press.

Melumad D.N., Mookherjee D. & Reichelstein S. (1995). Hierarchical Decentralization of Incentive Contracts. The Rand Journal of Economics, 26(4), 654-672.

Nykyforchyn I.V. (2017). Simulation of Active Systems with Dependent Incentives of Agents, Herold of Volyn Institute for Economics and Management, 19, 178-184. (in Ukrainian)