Author ORCID Identifier

Degree Year


Document Type

Thesis - Open Access

Degree Name

Bachelor of Arts


Computer Science


Kevin Woods


Prize-collecting Steiner tree, Algorithmic game theory, Steiner tree games, Facility location, Steiner tree, Nash equilibrium, Price of anarchy, Price of stability, PoA, PoS, Network design games


Prize-collecting Steiner tree is a network design problem in which a utility provider located at some position in a graph attempts to construct a network (subtree) of maximum profit based on the value of the vertices in the graph and the costs of the edges. I consider three network formation games where the players represent competing providers attempting to build networks in the same market. These games seek to preserve the key feature of Prize-Collecting Steiner tree, namely that players must each build a subtree that attempts to include customers who are of high value or are easy to reach. I analyze the price of anarchy and price of stability of each of these games.