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首页> 外文期刊>European Journal of Operational Research >Designing coalition-based fair and stable pricing mechanisms under private information on consumers' reservation prices
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Designing coalition-based fair and stable pricing mechanisms under private information on consumers' reservation prices

机译：在私人信息下设计基于联盟的公平和稳定定价机制，了解消费者预订价格

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摘要

We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers' reservation prices. At the upper-level of the Stackelberg game, the aggregator optimizes his daily price profile so as to reach a net targeted profit which is the maximum value guaranteeing that no consumer will leave the coalition - to contract with a conventional retailer considered here as a fixed alternative - while meeting fairness criterion imposed by the cost-sharing mechanism. At the lower-level, the consumers are asked to provide in day ahead an estimate of their base load hourly demand profile and to schedule their shiftable loads depending on the price signal sent by the aggregator. We provide algorithms that determine the unique price profile and consumer shiftable load schedules as functions of the reservation price estimates. The Stackelberg game between the aggregator and the consumers being repeated for a period of time, the aggregator has the possibility to update his estimates of the reservation prices relying on a feedback function which depends on the percentage of activated loads. A randomized algorithm for consumers' reservation price learning based on regret minimization is provided. For four cost-sharing mechanisms such as uniform allocation, stand-alone cost, Shapley value, separable and non-separable costs, we determine the closed form of the aggregator's optimal net targeted profit guaranteeing the stability of the coalition. We also determine conditions guaranteeing the core non-emptiness and prove that for a profit-maximizing aggregator, the stand-alone cost is always preferable to the Shapley value, which coincides with the uniform allocation. Furthermore, the optimal size of the coalition - in terms of the aggregator's profit - can be determined analytically when the Sha
机译：我们的聚合和消费者加入一个联盟，以减少他们的基本负荷需求的不可预测性导致的风险之间的关系模型，作为Stackelberg博弈配制成与对消费者的保留价格私人信息的数学二层程序。在Stackelberg博弈的上层处，聚集优化他每天的价格曲线，从而达到净针对性的利润，其最大值低保没有消费者会离开联盟 - 合同与此视为一种固定的传统零售商替代方案 - 同时满足公平性准则的成本分担机制，罚款。在下级，消费者被要求在未来的一天提供其基本负荷每小时需求分布的估计和安排取决于汇聚器发送的信号，价格的可移动的负载。我们提供的是确定唯一的价格曲线和消费可移动的负载调度作为预订价格测算的功能算法。被重复进行一段时间的聚合者和消费者之间的Stackelberg博弈，聚合必须更新自己的保留价格依靠依赖于激活负载百分比反馈功能的估计可能性。提供了消费者的基础上尽量减少遗憾预订价格为学习随机算法。对于四费用分摊机制，如统一调拨，单机成本，Shapley值，可分离和不可分离的成本，我们确定聚集的最佳网的封闭形式，有针对性的利润保障联盟的稳定。我们还确定保障的核心非空的条件和证明，对于一个追求利润最大化的聚合器，单机成本始终是最好的Shapley值，这与统一的分配重叠。此外，该联盟的最佳规模 - 在聚合的利润而言 - 可以分析决定的，当沙

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