A 3-PERSON GAME-THEORY MODEL ARISING IN STOCHASTIC INVENTORY CONTROL-THEORY

In this paper, we build a game theory model for a single-period invent ory problem where each of three retailers tries to determine his optim al order quantity. Their products are substitutable and have random de mands. Therefore, multiple direction demand transfers occur when one o r more retailers are sold out. It is shown that, by using Nash equilib rium, optimal decision exists for each retailer when they work indepen dently. The optimal order quantity in this case is larger than that un der the newsboy problem model. This is because substitution can be a s ource of sales and hence a justification for inventory. In situations where some retailer may act irrationally to inflict a damage on the ot hers, the defensive strategy for the latter is to totally ignore the e xistence of the irrational player. We also study the cooperation of re tailers by switching excess inventory to those who have excess demand both when side payments are and are not allowed. If side payments are not allowed, secure (Nash) strategies always exist for each retailer a nd cooperation will reduce inventory. The latter is especially true wh en the depreciation of value of the item and/or inventory carrying cos t are large. We give conditions for cooperation in both cases and show that although all-player cooperation is often feasible it may not alw ays be obtainable even if side payments are allowed.