On some problems in dynamic pricing, revenue management and cost and revenue allocation

拟议的研究将涉及以下三个问题/专题： (i)通常，人们假设，面对价格竞争，零售商遵循纳什均衡范式。 也就是说，如果价格偏离对他们来说是严格有利可图的，他们就会偏离价格。 然而，人们普遍认为，遵循纳什范式的零售商是短视的。 他们完全没有考虑到他们的偏差对其他参与者的影响，这最终将导致无差异产品的边际成本定价。 因此，我的目标之一是赋予零售商的远见，体现了最大的一致性集介绍Chwe（JET，1994），和它的可能的其他细化，并评估的影响，有远见的零售商的行为对价格和利润的多时期双寡头竞争模型。 (ii)本文的目标之一是研究一个多期双寡头模型，其中消费者被假定为不同的沿着商店忠诚度标准。一些消费者是商店忠诚的，而另一些是商店转换者，可能是由于他们的多样性寻求欲望。 解释，我计划赋予消费者的效用函数，占的好处，有各种服务提供商，我将调查的影响，这样的消费者的存在对价格和利润的多时期双寡头竞争模型。 (iii)我计划分析收入和成本分配问题，其中相应的合作博弈的核心是空的。 具体来说，我试图找到最小的额外收入或成本，必须由第三方贡献，这将导致一个非空的核心。 部分结果已经得到了一个合作游戏引起的路由问题的图，在那里我已经表明，最小的额外成本，这必须由第三方贡献，导致一个非空的核心，可以在立方时间中找到的球员数量时，在图中的最小边割的基数为3或更多。

The proposed research will address the following three issues/topics: (i) Ordinarily, it is assumed that, faced with price competition, retailers follow the Nash equilibrium paradigm. That is, they price-deviate if such a deviation is strictly profitable for them. However, it is well recognized that retailers who follow the Nash paradigm are short-sighted. They completely fail to consider the effect of their deviations on other players, which eventually would lead to pricing at the marginal cost for undifferentiated products. Accordingly, one of my objectives is to endow retailers with foresight, as embodied by the largest consistent set introduced by Chwe (JET, 1994), and its possible other refinements, and to evaluate the effect of the behavior of farsighted retailers on prices and profits in a multi-period duopoly competition model. (ii) One of my objectives is to study a multi-period duopoly model wherein consumers are assumed to differ along the store-loyalty criterion. Some of the consumers are store-loyal, while others are store-switchers, due perhaps to their variety seeking desires. Explicitly, I plan to endow consumers with a utility function which accounts for the benefits of having a variety among service providers, and I will investigate the effect of the existence of such consumers on prices and profits in a multi-period duopoly competition model. (iii) I plan to analyze revenue and cost allocation problems in which the core of the corresponding cooperative game is empty. Specifically, I seek to find the smallest additional revenue or cost that has to be contributed by a third party, and which would lead to a non-empty core. Partial results were already obtained for a cooperative game induced by a routing problem on a graph, where I have shown that the smallest additional cost, that has to be contributed by a third party, leading to a non-empty core, can be found in cubic time in the number of players when the minimal edge-cutest in the graph is of cardinality three or more.