In this work we propose a new cooperation strategy between connected autonomous vehicles in on-ramps merging scenarios and we implement the cut-in risk indicator (CRI) to investigate the safety effect of the proposed strategy. The new cooperation strategy considers a pair of vehicles approaching an on-ramp. The strategy then makes decisions on the target speeds/accelerations of both vehicles, possible lane changing, and a dynamic decision-making approach in order to reduce the risk during the cut-in manoeuvre. In this work, the CRI was first used to assess the risk during the merging manoeuvre. For this purpose, scenarios with penetration rates of autonomous vehicles from 20% to 100%, with step of 10%, both connected and non-connected autonomous vehicles were evaluated. As a result, on average a 35% reduction of the cut-in risk manoeuvres in connected autonomous vehicles compared to non-connected autonomous vehicles is obtained. It is shown through the analysis of probability density functions characterising the CRI distribution that the reduction is not homogeneous across all indicator values, but depends on the penetration rate and the severity of the manoeuvre.