Applications that include real-time video delivery are demanding on network performance, while the various network resources are usually constrained. This fact boosts the need for efficient resource management, aiming at the amelioration of the video quality that reaches the end-user. The present paper considers a wireless direct sequence code division multiple access visual sensor network, which employs a cross-layer design. The objective is the maximization of the nodes' utilities under the constraints of a maximum bit rate and a maximum power level for each node. In this vein, the Kalai-Smorodinsky bargaining solution is applied, which is geometrically derived from the graphical representations of the utility sets, under a centralized topology. Ultimately, we have to deal with an optimization problem that concerns the optimal determination of the source coding rates, channel coding rates, and power levels of all nodes of the network, under certain modeling conditions. The experimental results provided by the Kalai-Smorodinsky bargaining solution are compared with results using the Nash bargaining solution and two other schemes that aim at the maximization of an unweighted and a weighted version of the total network utility, respectively. A metric that captures fairness and performance issues is used in order to compare the performance of the schemes. The results are also evaluated in terms of the total consumed power relative with the total achieved utility.