In this scientific article the main elements of game theory are analyzed, the achievements of domestic and foreign scientists devoted to the consideration of such theory are investigated. The expediency of involving in the practical activity of the civil service in the system of judicial authorities effective methods used in the field of business and consisting in the use of game technologies, which have proven their effectiveness in terms of providing quality services. It is focused on the fact that game theory can play a key role in the decision-making process, however, it is important to strictly adhere to the limits of its application. Possible conflict situations in the work of civil servants of the justice system are formulated and it is investigated that in conflict conditions each so-called participant of the game makes his course, i.e. chooses his strategy, as a result of which the relevant conflict situation is outlined and a set of strategies of all players. Some examples of the use of elements of game theory are given and the content of certain types of strategies is revealed. In particular, a strategy is described, which is denoted by the term "screening". Taking into account the definition of ways to modernize the civil service, the need to include in standardized training programs for civil servants of the justice system category "B" training course, which will include the basic principles of game theory for their active use in conflict, skills to compromise in relationships with visitors to the court - recipients of court services, selection of the right strategy, consideration of theoretical and game modeling of personnel management tasks, focusing on the ability to obtain and timely provide the necessary information to create a new civil service in the judiciary that meets international standards.