The paper reveals the basis and constraints for applying the discount of 1/8-th fines for a company that has violated the antitrust law, but previously introduced an antitrust compliance program. Here is an example of the following idea implementation: a company gets an opportunity for fines discounts in case of law violation if it elaborates and implements a set of internal institutions to abide by the corresponding law. To reveal the role of the corporate compliance programs as a means of forming credible commitments on the part of companies was one of the goals of the research. So, situations on creating incentives for companies not to commit anticompetitive actions were considered and analyzed, as well as the deterrence effects of the legal system and the issues of I and II types of errors in enforcement were explained. For this reason differences between the antitrust compliance programs and leniency programs are demonstrated. The applicability of the comparative negligence rule is also discussed. Elements of a model are introduced that reflect the possibilities of not only a fair use of the compliance programs, but also of an opportunistic behavior of the actors, including the antitrust authority. There is no guarantee that the antitrust compliance program should lead to equilibrium in the strategic interaction with the choice of “minimal control” by the antimonopoly agency.