销售可分割物品的线性公布定价机制的收益差距界限
Bounds on the revenue gap of linear posted pricing for selling a divisible item
AI总结：
本文研究可分割物品销售的线性公布定价机制，在贝叶斯凹估值设定下证明其与最优机制的收益差距仅对数依赖于估值函数的自然参数和买家数量，从而刻画了简单定价机制的能力边界。
摘要：
向潜在买家销售完全可分割的物品是一项基本任务，在定价通信带宽和云计算服务方面具有明显的应用。令人惊讶的是，尽管关于单物品拍卖的文献十分丰富，但在销售可分割物品时实现收益最大化是一个远未被充分理解的目标。我们引入一个贝叶斯设定，其中潜在买家具有凹的估值函数（针对每种可能的物品份额定义），这些估值函数根据已知的概率分布随机选取。扩展顺序公布定价范式，我们聚焦于使用线性定价的机制，即对整件物品收取固定价格，对其份额按比例收取价格。我们的目标是通过界定这些机制中最佳机制所能达到的期望收益与在买家行为受到温和限制的假设下任何机制所能达到的最大期望收益之间的差距，来理解此类机制的能力。在概率分布满足正则性假设的条件下，我们证明这一收益差距仅对数地依赖于一个刻画估值函数和智能体数量的自然参数。我们的结果通过界定一个数学规划的目标值而得到，该数学规划在线性定价收益约束下最大化最优收益的事前松弛。
英文摘要：
Selling a perfectly divisible item to potential buyers is a fundamental task with apparent applications to pricing communication bandwidth and cloud computing services. Surprisingly, despite the rich literature on single-item auctions, revenue maximization when selling a divisible item is a much less understood objective. We introduce a Bayesian setting, in which the potential buyers have concave valuation functions (defined for each possible item fraction) that are randomly chosen according to known probability distributions. Extending the sequential posted pricing paradigm, we focus on mechanisms that use linear pricing, charging a fixed price for the whole item and proportional prices for fractions of it. Our goal is to understand the power of such mechanisms by bounding the gap between the expected revenue that can be achieved by the best among these mechanisms and the maximum expected revenue that can be achieved by any mechanism assuming mild restrictions on the behavior of the buyers. Under regularity assumptions for the probability distributions, we show that this revenue gap depends only logarithmically on a natural parameter characterizing the valuation functions and the number of agents. Our results follow by bounding the objective value of a mathematical program that maximizes the ex-ante relaxation of optimal revenue under linear pricing revenue constraints.
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