An infinite horizon multi-echelon supply chain inventory problem has been analysed using stochastic analytical methods. A first-order autoregressive demand pattern is assumed and each player adopts the order-up-to (OUT) policy to place orders on its suppliers/production facilities. The results indicate three principles governing the dynamics of the supply chains. They are: " Altruistic Behaviour principle. " Intervention Information Sharing principle. " Time Compression principle. Each principle can significantly contribute to lower inventory related costs and a reduction in the bullwhip effect. The Altruistic Behaviour principle revealed herein shows that a significant amount of benefit comes from the player doing what is the best for the overall supply chain, rather than what is the best for local cost minimisation. This insight suggests that a sequence of optimal policies is not globally optimal. A supply chain integration scheme is presented that exploits this principle. As the ordering process contains complete information of market demand, there are no benefits of the sharing market demand information with upper echelon players. In contrast, sharing intervention event information has the potential to bring a large benefit to the upper echelon players for the reducing inventory costs. This leads to the Intervention Information Sharing principle. Further analysis reveals the Time Compression principle, which is that the level of the supply chain has no impact upon both the bullwhip effect and the variance of the total net stock level. The bullwhip is determined by the accumulated leadtime from the customer and the local replenishment lead-time. The variance of the total net stock level can be expressed as the variance of forecast error over the accumulated replenishment lead-time and is independent from the number of echelons to the end consumer. A new method is presented which enables the complicated analytical expressions of variances (or standard deviations) of net stock levels and orders in a multi-echelon supply chain model to be obtained without a specification of lead-time.