When claims happen in the process of construction, in order to determine an amount compensated to the contractor, normally the owner and the contractor have to negotiate with each other or even refer to mediation and arbitration, which is a bargaining process as a whole. This paper interprets the discount factor in this process as a kind of hidden cost and sets out its three influencing factors. Then by developing and solving a dynamic-game model with the Rubinstein Bargaining-game Theory the best quotes in each stage of the bargaining process are proposed for the two parties. Based on these, the paper concludes the key factors affecting the bargaining process and the two parties' quotes, including their discount factors, mediation and arbitration costs and so on. Several suggestions for the two parties solving claim problems rationally are summarized at the end.