This paper considers the deployment of a cognitive radio scheme in wireless sensor networks to achieve (1) fair spectrum allocation, (2) maximum spectrum utilization, and (3) priority-based sensor transmissions, while (4) avoiding unnecessary spectrum handover (or handoff). This problem is modelled as a bi-objective optimization problem. We apply modified game theory and a cooperative approach to identify an approximate optimal solution in reasonable time. We perform a series of numerical experiments to show that our scheme achieves fair spectrum allocation (in terms of proportional fairness) while observing transmission priorities and minimizing unnecessary spectrum handover.