This study applies the Shapley value within the context of class-group based peer assessments by treating it as a cooperative game and giving fairness to each group member to cushion the effect of coalitions. Based on scenario analysis, the Shapley Value method is used to identify the fair marks which should be given/allocated to individuals with in groups where there is uneven participation. Scenarios are presented using two and three student member cases with situations under pinning the free rider problem. The Shapley value concept as applied in this study provides what may be viewed as a contribution consistent mark allocation for group assignments.