Minimum Cost Spanning Tree Games

Abstract

Four geographically separated communities in the desert, Wasteland Village, Xactustown, Yuccaville, and Zun Valley, are desperate. Their water resources are running out and they don’t see a way to survive. If nothing happens they will have to leave their villages to settle somewhere else. Then, just when they think that everything is lost, a spring is found not too far away. At first there is much rejoicing, but then they have to sit down and decide on a way to build a water distribution system that is as cheap as possible. It is quite evident that to connect each community to the spring is not the cheapest way. In table 6.1 the costs involved in building a water distribution system are given in $10,000. After some analysis they realize that the cheapest thing to do is to build pipes connecting Wasteland Village and Yuccaville directly to the spring, while Zun Valley has a pipe connecting it to Wasteland Village and Xactustown has a pipe connecting it to Zun Valley. Now they have to settle on a way to distribute the costs. The total costs are 6.