In this paper a game is used to compare the licensing of a cost reduction innovations under lost profits (LP) and unjust enrichment (UE), both damage rules that are used by courts in the calculation of damages when a patent has been infringed. The market is composed by two homogeneous firms that compete in quantities (Cournot), both firmas produces a homogeneous good. One of the firms (patent holder) develops a cost reduction innovation (drastic or non-drastic) and got a patent for this innovation. Under the shadow of probabilistic property rights, It is founded that licensing by using royalty rate is preferred compared with fixed fees, also it is observable little licensing (just big innovations). By comparing LP against UE, it is concluded that for drastic innovation the patentee and licensee are better off under LP. However social welfare is greater under UE. In the case of a non drastic innovation the results do not show a rule better than the other one.