The subject of this article is the application of game theory (GT) to solve the problem occurring in the management of construction contracts. One of the fundamental reasons for disputes between the investor (IN) and the general contractor (GC) is payment for supplementary works—an additional expenditure incurred by GC that was not planned at the tender stage. If IN delays signing the annex to the contract and rejects any financial and timeframe-related claims, GC usually considers one of the two strategies: to stop works or to continue works without the annex and the guarantee of payment for additional works. IN also analyzes the consequences of adopting one of the two strategies: not to sign the annex, or to sign the annex and pay for the additional work. The aim of the presented game is to indicate the optimal strategy from the GC point of view in the conflict situation with IN. The article defines the background of the problem, the cause of the dispute, and formulates a theoretical model of the game.