We consider a distribution system consisting of a System Administrator (SA) and N retailers managed under dynamic allocation and static routing policies. We study the system under two scenarios: (a) the up‐to‐date information scenario, under which the SA has access to the inventory levels at the retailers in real time and makes the replenishment and allocation decisions based on these information, aiming to minimize total supply chain cost; (b) the retailer‐reporting scenario, under which the SA makes the replenishment and allocation decisions based on the information reported by the retailers. Under the retailer‐reporting scenario, the retailers compete against each other by reporting their inventory levels falsely to get the desired allocations, which minimize the retailers’ expected cost. For N=2 retailers, we show that, in general, reporting truthfully does not minimize either retailer's expected cost/cycle over their respective replenishment/allocation cycles, and that the sum of the retailers' expected cost/cycle is strictly greater than in the up‐to‐date information scenario. We then show that by including a particular transfer‐payment between the two retailers, truth‐telling is a Bayesian equilibrium, and that the same system expected cost/period as in up‐to‐date information scenario can be achieved.
