The paper considers two-stage game-theoretic models of the project management contract with a random duration of tasks. In the first stage, the Principal signs the contract for task execution in which he determines the amount and regime of payments to each of the contractors; in the second stage, the contractors choose their own work rates. The optimal amount of payments and the expected completion time of the project are estimated. The characteristics of the optimal contract for each payment regime are numerically simulated. In accordance with the comparative analysis of the simulation results, the project manager (Principal) benefits from choosing the contract with different payments for the contractors and the payment regime upon completion of tasks.