In this paper, we propose a market based dynamic bit allocation scheme for target tracking in energy constrained wireless sensor networks using quantized data. We model the dynamic bit allocation problem as a market based policy where the fusion center is the customer and sensors are the producers of the market. The fusion center releases the energy to purchase m-bit measurements from sensors in such a way that the trace of the posterior Cramér-Rao lower bound (PCRLB) on the mean squared error (MSE) is minimized. Sensors then compete to purchase the energy released from the fusion center and produce their m-bit quantized measurements which maximize their profit. Simulation results show that the market based dynamic bit allocation scheme achieves tracking performance close to the case where all the sensors report their most accurate information to the fusion center while the market based dynamic bit allocation scheme releases energy which is significantly less than the energy required to transmit all sensor data to the fusion center.