报童库存集中化中的动态实现博弈
Dynamic Realization Games in Newsvendor Inventory Centralization
AI总结：
针对报童库存集中化中的动态实现博弈，提出基于Lehrer规则的重复成本分配方案，证明成本子序列几乎必然收敛到最小二乘值或期望博弈的核，并推广至更一般情形。
摘要：
考虑一个由 n（>1）家商店组成的集合 N，每家商店面临单物品、单周期的非确定性需求，如同经典报童模型中仅包含持有成本和惩罚成本的情形。假设存在一个风险共担的单仓库集中库存订购选项。在集中库存订购中分配成本对应于将其建模为一个合作成本博弈，其中参与者为各商店。已有研究表明，当持有成本和惩罚成本对所有商店子集均相同时，基于最优期望成本的博弈具有非空核（Hartman et al., 2000; Muller et al., 2002）。本文研究一个基于需求实现的库存集中化博弈，该博弈即使在惩罚成本和持有成本相同的情况下，通常也具有空核（Hartman and Dror, 2005）。我们基于Lehrer（2002a）引入的分配过程，提出了一种针对动态实现博弈的重复成本分配方案。我们证明，基于Lehrer规则的动态实现博弈过程中的成本子序列几乎必然收敛到最小二乘值或期望博弈的核。我们将上述结果扩展到更一般的动态成本博弈，并放宽了不同阶段参与者需求序列的独立性假设。
英文摘要：
Consider a set N of n (>1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et. al., 2000, Muller \textit{et. al.}, 2002). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror, 2005). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer's rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players' demands at different stages.
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