When multiple video sources are live-encoded and transmitted over a common wireless network, each stream needs to adapt its encoding parameters to wireless channel fluctuations, so as to avoid congesting the network. We present a stochastic system model for analyzing multi-user congestion control for live video coding and streaming over a wireless network. Variations in video content complexities and wireless channel conditions are modeled as independent Markov processes, which jointly determine the bottleneck queue size of each stream. Interaction among multiple users are captured by a simple model of random traffic contention. Using the model, we investigate two distributed congestion control policies: an approach based on stochastic tic dynamic programming (SDP) and a greedy heuristic. Compared to fixed-quality coding with no congestion control, performance gains in the range of 0.5-1.3 dB in average video quality are reported for the optimized schemes from simulation results.