The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth Graphs

The Stackelberg Minimum Spanning Tree Game

We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum…

Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game

Let be given a graph $G=(V,E)$ whose edge set is partitioned into a set $R$ of \emph{red} edges and a set $B$ of \emph{blue} edges, and assume that red edges are weighted and form a spanning tree of $G$. Then, the \emph{Stackelberg Minimum Spanning Tree} (\stack) problem is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. \stack \ is known to be \apx-hard already when the number of distinct red weights is 2. In this paper we analyze some meaningful specializations and …

使用拆分和合并解决树上的斯塔克尔伯格顶点覆盖问题

Solving Stackelberg Vertex Cover on trees using split and join

研究树上的斯塔克尔伯格顶点覆盖问题，提出三种新算法，包括一般树的伪多项式算法、特定树的强多项式算法和树的FPT算法，基于引理拆分实例，引入承诺概念，还证明带承诺问题是弱NP完全的。

Stackelberg Network Pricing Games

We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of $m$ priceable edges in a graph. The other edges have a fixed cost. Based on the leader's decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader's prices. The leader receives as revenue the total amount of prices paid by the followers for priceable edges in their solutions, and the problem is to find revenue maximizing…

基于神经流表示的Stackelberg博弈黎曼流形学习

Riemannian Manifold Learning for Stackelberg Games with Neural Flow Representations

针对Stackelberg一般和博弈的在线学习问题，提出基于神经归一化流的微分同胚映射构建Stackelberg黎曼流形的框架，结合线性老虎机算法实现遗憾最小化，理论验证并实证其在多领域优于基线的性能。

Spanning connectivity games

The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected, unweighted multigraph, where edges are players. We examine the computational complexity of computing the voting power indices of edges in the SCG. It is shown that computing Banzhaf values and Shapley-Shubik indices is #P-complete for SCGs. Interestingly, Holler indices and Deegan-Packel indices can be computed in polynomial time. Among other results, it is prove…