In recent years, improved wireless technologies have enabled the low-cost deployment of large numbers of sensors for a wide range of monitoring applications. Because of the computational resources (processing capability, storage capacity, etc.) collocated with each sensor in a wireless network, it is often possible to perform advanced data analysis tasks autonomously and in-network, eliminating the need for the postprocessing of sensor data. With new parallel algorithms being developed for in-network computation, it has become necessary to create a framework in which all of a wireless network's scarce resources (CPU time, wireless bandwidth, storage capacity, battery power, etc.) can be best utilized in the midst of competing computational requirements. In this study, a market-based method is developed to autonomously distribute these scarce network resources across various computational tasks with competing objectives and/or resource demands. This method is experimentally validated on a network of wireless sensing prototypes, where it is shown to be capable of Pareto-optimally allocating scarce network resources. Then, it is applied to the real-world problem of rupture detection in shipboard chilled water systems.