Abstract: Study the inventory competition among n-retailers selling the homogeneous brand products of 2 manufacturers under the stochastic inventory-dependent demand.  The EPEC (equilibrium problem with equilibrium constrains) model for agentprofit-maximization, Nash equilibrium model for brand-profit-maximization and Nash equilibrium model for channel-profitmaximization are set up, together with their solving process, by using the equilibrium analysis method. It shows that the order-quantity of agent-profit-maximization is lowest, so that the profits of each brand and each channel under agent-profit-maximization mode are lower than those under brand-profit-maximization mode and channel-profit-maximization mode respectively. Two buy-back contracts are put forward. The order-quantities under agent-profit-maximization mode with two contracts are as same as those under brand-profit-maximization mode and channel-profit-maximization mode respectively. Finally, a numerical simulation analyzes the reasonability of models and validity of contracts.

Key words: supply chain network, inventorydependent demand, EPEC (equilibrium problem with equilibrium constrains), Nash equilibrium