论文标题
在多需求组合市场中的最佳动态定价的两步方法
A Two-Step Approach to Optimal Dynamic Pricing in Multi-Demand Combinatorial Markets
论文作者
论文摘要
在线市场是日常生活的一部分，其规则受算法的约束。假设参与者本质上是自私的，设计精良的规则可以帮助增加社会福利。在线市场的许多算法都是基于价格：卖方负责发布价格，而买家进行购买，这是鉴于张贴的价格最有利可图的。为了调整市场，允许卖方在特定时间点更新价格。 发布的价格是设计市场的直观方式。尽管每个买家都自私地行动，但卖方的目标通常被认为是社会福利最大化的目标。伯杰（Berger），伊甸园（Eden）和费尔德曼（Feldman）最近考虑了一个市场案例，只有三名买家，每个买家都有固定的商品要购买的商品，而购买的商品的利润是捆绑包中物品的利润之和。对于此类市场，Berger等。 al。表明卖方可以通过在每个买家到达之前动态更新发布的价格来最大化社会福利。 Bérczi，Bérczi-Kovács和Szögi表明，当每个买家准备购买最多两个商品时，社会福利也可以最大化。 在更普遍的情况下，我们研究了发布价格的功能，并具有动态更新。首先，我们证明了Berger等的结果。 al。可以从三到四个买家中概括。然后，我们表明，当每个买家准备购买最多三件商品时，可以将Bérczi，Bérczi-Kovács和Szögi的结果推广到案件中。我们还表明，只要最多有两个分配最大化社会福利，就可以使用动态定价。
Online markets are a part of everyday life, and their rules are governed by algorithms. Assuming participants are inherently self-interested, well designed rules can help to increase social welfare. Many algorithms for online markets are based on prices: the seller is responsible for posting prices while buyers make purchases which are most profitable given the posted prices. To make adjustments to the market the seller is allowed to update prices at certain timepoints. Posted prices are an intuitive way to design a market. Despite the fact that each buyer acts selfishly, the seller's goal is often assumed to be that of social welfare maximization. Berger, Eden and Feldman recently considered the case of a market with only three buyers where each buyer has a fixed number of goods to buy and the profit of a bought bundle of items is the sum of profits of the items in the bundle. For such markets, Berger et. al. showed that the seller can maximize social welfare by dynamically updating posted prices before arrival of each buyer. Bérczi, Bérczi-Kovács and Szögi showed that the social welfare can be maximized also when each buyer is ready to buy at most two items. We study the power of posted prices with dynamical updates in more general cases. First, we show that the result of Berger et. al. can be generalized from three to four buyers. Then we show that the result of Bérczi, Bérczi-Kovács and Szögi can be generalized to the case when each buyer is ready to buy up to three items. We also show that a dynamic pricing is possible whenever there are at most two allocations maximizing social welfare.
