A consignment system where suppliers cannot verify retailer's sales reports

Newspapers are often sold through stores via consignment arrangements, which involve vendor (publisher) managed inventory and revenue sharing. Since retailers are not required to actually return unsold copies, it is said that some of them occasionally under-report sales. That hurts the publisher on the short run and could also interfere with his rational stocking decisions as these are based, to some extent, on previous sales reports. We construct a discounted dynamic framework for the retailer's optimal reporting as a function of the publisher's delivery-response function to these reports, and a similar average-cost model. It turns out the optimal report does not depend on actual sales. We then show that the publisher's resulting delivery response function is the same as it would be in an integrated system. Thus the retailer's untruthful behavior actually causes the system to behave optimally. Had the retailer been verifiably truthful, the system would not be coordinated.