Game theory approach for supply chains optimization in case of deterministic demand

In this paper game theoretic mathematical models of inventory systems are treated. We consider a market, where several distributors are acting. Each distributor has warehouse for storage goods before supply to customers. Assume that demand for their goods has deterministic nature and depends on total supply or on prices of distributors. So we will consider quantitative and price competition among distributors. Distributors are considered as players in non-cooperative game. First we treat quantitative competition in context of model of Cournot. Then to consider price competition we use modified model of Bertrand. For modeling of control of inventory system we use the relaxation method of inventory regulation with admission of deficiency.