Wireless sensor networks for control and moni- toring applications introduce critical constraints on the design of multiple access schemes. Controlling dynamic processes requires that priority must be given to critical systems for the use of the wireless medium. Tournaments in the medium access control (MAC) layer are presented as a way to evaluate priorities and assign channel resources in a distributed manner. The priorities are dynamically assigned based on the attention that each data packet requires. A mathematical formulation of attention is presented together with the corresponding performance analysis of the multiple access scheme. Priorities based on the attention emphasize the information content in the data to be transmitted and the related process dynamics. It is shown that under certain conditions, the performance of this distributed scheme converges to a scheduling policy based on minimizing the per-sample variance of the error in the estimates obtained with limited communication resources. Sustainable data rates for a cluster of linear processes are also derived.