PurposeThis research uses the evolutionary game model theory to explore how to make decisions to maximize their own interests in the process of project claims from the perspective of small and medium-sized contractors in the construction industry.Design/methodology/approachThis study defines the discount factor in the claim process based on the characteristics of construction claims and provides a specific calculation method. The paper analyzes the matching degree between the evolutionary game model and the process of construction claims. Further, the discount factor is introduced to construct an evolutionary game model of engineering claims with the goal of maximizing the contractor’s benefits.FindingsThe results of this study show that in the situation (C*d1-nC1*d1>0, v2-v1-g>0) and (C*d1-nC1*d1>0, v2-v1-g<0), the contractor claim decision-making strategy is a truthful claim, while in the situation (C*d1-nC1*d1<0, v2-v1-g>0) and (C*d1-nC1*d1<0, v2-v1-g<0), the contractor claim decision-making strategy is a high-price claim. The discount factor will affect the decision-making rate. It is noted that the fines and the explicit costs received during the contractor’s high-priced claim process exhibit a positive correlation with the rate of truthful claim decision-making by contractors. Meanwhile, the final revenue of high-priced claims by contractors shows a positive correlation with the rate of high-priced claim decision-making by the sensitivity analysis.Research limitations/implicationsThe author simulates the process of solving the actual claim problem through the evolutionary game model in engineering claims. It is hoped that researchers will collect empirical cases and compare the actual case solutions with the model solutions to further revise the model in future studies, an evolutionary game model of engineering claim decision-making with interference factors can be constructed to analyze the evolutionary stability. Secondly, the single factor sensitivity analysis of individual parameters is carried out in this paper, and the influence of multiple factors on claim decisions can be further analyzed in the later research.Practical implicationsThe analysis of the claim process based on the evolutionary game model is conducive to the contractor’s rapid claim decision-making. The introduction of the discount factor to analyze the claim process is more conducive to the accuracy of the contractor’s claim decision.Originality/valueThe proposed model provides a supplement to the existing studies on dynamic construction claim decision-making. The claim decision is conducive to controling cost for the contractor, improving the contractor’s management level and developing a healthy construction market.