The Competitive Facility Location Problem in a Duopoly: Connections to the 1-Median Problem
The Competitive Facility Location Problem in a Duopoly: Connections to the 1-Median Problem
复制标题
双头垄断中的竞争设施选址问题：与 1 中值问题的联系
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
N. Stier
中科院分区：
文献类型：
--
作者：
Daniela Sabán;N. Stier
我们考虑网络上的一个竞争设施选址问题，其中消费者位于顶点上，并希望连接到最近的设施。基于这一点，竞争参与者将他们的设施选址在能获取最大可能市场份额的顶点上。1991年，艾斯尔特（Eiselt）和拉波特（Laporte）建立了双寡头设施选址博弈的纳什均衡与1 - 中位数问题的解之间的第一种关系。他们表明，在一棵树中总是存在一个均衡，因为当且仅当两个参与者都选择那棵树的一个1 - 中位数时，一个选址组合处于均衡状态[4]。在这项工作中，我们进一步探究1 - 中位数问题的解与均衡组合之间的关系。我们表明，如果在一个环中存在一个均衡，那么两个参与者都必须选择1 - 中位数问题的一个解。对于一些其他类别的图，例如拟中位数图、中位数图、赫利图和强弦图，我们也得到了相同的性质。最后，我们证明了后一类图的逆命题，即如同树的情况一样，强弦图的任何中位数都是一种能导致均衡的获胜策略。
We consider a competitive facility location problem on a network, in which consumers are located on the vertices and wish to connect to the nearest facility. Knowing this, competitive players locate their facilities on vertices that capture the largest possible market share. In 1991, Eiselt and Laporte established the first relation between Nash equilibria of a facility location game in a duopoly and the solutions to the 1-median problem. They showed that an equilibrium always exists in a tree because a location profile is at equilibrium if and only if both players select a 1-median of that tree [4]. In this work, we further explore the relations between the solutions to the 1-median problem and the equilibrium profiles. We show that if an equilibrium in a cycle exists, both players must choose a solution to the 1-median problem. We also obtain the same property for some other classes of graphs such as quasi-median graphs, median graphs, Helly graphs, and strongly-chordal graphs. Finally, we prove the converse for the latter class, establishing that, as for trees, any median of a strongly-chordal graph is a winning strategy that leads to an equilibrium.