This work concerns the evaluation and rewarding of vendors who manage inventories of items they sell at different retailers, for their relative performance in forecasting demand. The specific scenario which motivated us has to do with a dairy/cheese-wholesaler who deploys distributors each of whom manages the inventories of dairy products at different supermarkets and deli-stores (VMI), which have a revenue-sharing arrangement with the dairy. A distributor visits each of his stores once a week, removes expired items and stocks the shelf with quantities of his choice. The dairy compiles distributor and item specific reports pertaining to weekly sales and expirations. The question is how can one tell which distributor did a better job? A good distributor is one with few overages (expirations) and few underages (sales lost due to the shortages). We thus suggest giving a larger bonus to the distributor which had less overages and underages and examine the results of such policy. This work presents three different models of prize awarding games between two distributors. Each distributor’s strategy is his stock level. An equilibrium is a combination of strategies, so that no distributor can improve his expected reward by choosing a different level of stock. In the first model the dairy gives a larger bonus to the distributor who caused less overage and underage costs. In the second model it gives a larger bonus to the distributor who had less overages and underages. In the third model the dairy gives a larger bonus to the distributor who caused less normalized overage and underage costs.
*Co-authored with Oshry Azriel