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Multi-period inventory games with information update

机译：具有信息更新的多期间库存游戏

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This paper addresses the multi-period inventory game of two substitutable products with learning, in which the demand distribution form in each period is known but one or more parameters are unknown in advance. The retailers update the estimates of the unknown parameters using the historical demand information as the transaction proceeds. At each period, the retailers check the initial inventories and update the forecasts about their demands first. Then they place the orders, which are delivered immediately. Finally the demands are realized and satisfied by the available inventories. The unsatisfied demand of one retailer switches to another and is satisfied by the other's left inventory. Unsatisfied demand is lost and the excess inventories incur a holding cost. All the information is common knowledge. The objectives of the two retailers are to make proper ordering decisions to maximize their total expected discount profits respectively. We model the problem as a dynamic Bayesian game with multi dimension state-space. We give the conditions under which the state-space can be reduced. We prove the existence and uniqueness of Nash equilibrium and show that the equilibrium ordering strategy is the base-stock policy, the computation of the base-stock levels can be reduced to a game with one dimension state-space. Moreover, for the case with perishable product, the computation of the base stock levels can be reduced to the Newsboy game. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文研究了具有学习能力的两种可替代产品的多周期库存博弈，其中每个时期的需求分布形式是已知的，但一个或多个参数事先是未知的。随着交易的进行，零售商使用历史需求信息更新未知参数的估计值。在每个阶段，零售商都会检查初始库存并首先更新有关其需求的预测。然后他们下订单，这些订单将立即交付。最终，可用库存实现并满足需求。一个零售商的不满意需求切换到另一个零售商，并由另一个零售商的剩余库存来满足。失去了不满意的需求，过多的库存产生了持有成本。所有信息都是常识。两家零售商的目标是做出适当的订购决策，以分别最大化其预期的折扣总利润。我们将问题建模为具有多维状态空间的动态贝叶斯博弈。我们给出了可以减少状态空间的条件。我们证明了纳什均衡的存在性和唯一性，并证明了均衡排序策略是基本股票策略，基本股票水平的计算可以简化为一维状态空间的博弈。此外，对于易腐烂的产品，基本库存水平的计算可以简化为Newsboy游戏。 （C）2016 Elsevier B.V.保留所有权利。

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