The crucial rule of Grid systems is intentional resource sharing among individual Grid users. However, there is an intrinsic friction between individual prudence and collective welfare that threatens the viability of these systems. Grid systems have emerged as a popular alternative to traditional clientserver architectures for resources distribution and sharing. Different academic studies have observed high levels of free-riding in various Grid systems, leading some to suggest the imminent collapse of these systems as viable resource sharing mechanism. This observable fact was due to hidden-action, hidden information as well as betrayer of co-operation and confidence among the selfish participating users with diverse malicious intentions. In Grid system, the supply and demand theory is symbiotic since the supplier of resources to other users within the system also demands for resources supplied by others. Generally, this paper investigated into the intersection of economics and computer science in the designing of Grid systems that consisting of rational participants with diverse and egocentric interests. This diversity behaviour usually led to free-riding which is a great hindrance to the achievement of the objectives of Grid system. This paper therefore develops an analytic model to analyze the behaviour of different users with different intentions in Grid system. Reciprocity-based schemes that premised on incentive mechanisms and user’s co-operation was applied to address the problem of free-riding. In all, forty-five simulations were carried out under each parameter (i.e. storage space, memory and bandwidth). Before arriving at the result, various values of α used are; 0.05, 0.1, 0.5, 0.9, 1.0, 1.05, 1.1, 1.5 and 2.0 where α is the resource utilization determinant of the system. The proposed scheme performed optimally when α = 1. In the control experiments, it was observed that immediately the value of α is greater than 1, no matter how small, there exists contention and free-riding eventually ensue in the system. However, the value of α under the proposed scheme can never be greater than 1; since 0 < α ≤ 1. This circumstance is being controlled and managed by the formulated policy engine and access control mechanism of the scheme.