This article describes how to solve the game problem of assigning staff to work on projects based on the ontological approach. The stochastic game algorithm for colouring an undirected random graph has been used to plan project implementation. The stochastic game mathematical model has been described, and the self-learning Markov method has been used for its solution. It is highlighted that the goal of the players is to minimize the functions of average losses. The Markov recurrent method that provides the adaptive choice of colours for the vertices of the random graph based on dynamic vectors of mixed strategies, the values of which depend on the current losses of players has been used. A computer experiment was carried out, which confirmed the convergence of the stochastic game for the problem of colouring the random graph. In conclusion. the possibility of defining the procedure for appointing staff to implement projects has been justified.