Stackelberg Vertex Cover on a Path
Katharina Eickhoff, Lennart Kauther, Britta Peis

TL;DR
This paper studies the Stackelberg Vertex Cover game on paths, providing a linear-time dynamic programming solution for the leader's optimal pricing problem in this specific graph class.
Contribution
It introduces a novel linear-time dynamic programming algorithm for solving StackVC on path graphs, expanding understanding of this game beyond bipartite cases.
Findings
Linear-time algorithm for StackVC on paths
Efficient computation of optimal leader prices
Extension of StackVC analysis to path graphs
Abstract
A Stackelberg Vertex Cover game is played on an undirected graph where some of the vertices are under the control of a \emph{leader}. The remaining vertices are assigned a fixed weight. The game is played in two stages. First, the leader chooses prices for the vertices under her control. Afterward, the second player, called \emph{follower}, selects a min weight vertex cover in the resulting weighted graph. That is, the follower selects a subset of vertices such that every edge has at least one endpoint in of minimum weight w.r.t.\ to the fixed weights, and the prices set by the leader. Stackelberg Vertex Cover (StackVC) describes the leader's optimization problem to select prices in the first stage of the game so as to maximize her revenue, which is the cumulative price of all her (priceable) vertices that are contained in the follower's solution. Previous…
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Taxonomy
TopicsEconomic theories and models · Game Theory and Applications · Auction Theory and Applications
